Abstract: Implementation of a commercial application to a
grid infrastructure introduces new challenges in managing the
quality-of-service (QoS) requirements, most stem from the fact
that negotiation on QoS between the user and the service provider
should strictly be satisfied. An interesting commercial application
with a wide impact on a variety of fields, which can benefit from
the computational grid technologies, is three–dimensional (3-D)
rendering. In order to implement, however, 3-D rendering to a
grid infrastructure, we should develop appropriate scheduling
and resource allocation mechanisms so that the negotiated (QoS)
requirements are met. Efficient scheduling schemes require
modeling and prediction of rendering workload. In this paper
workload prediction is addressed based on a combined fuzzy
classification and neural network model. Initially, appropriate
descriptors are extracted to represent the synthetic world. The
descriptors are obtained by parsing RIB formatted files, which
provides a general structure for describing computer-generated
images. Fuzzy classification is used for organizing rendering
descriptor so that a reliable representation is accomplished which
increases the prediction accuracy. Neural network performs
workload prediction by modeling the nonlinear input-output
relationship between rendering descriptors and the respective
computational complexity. To increase prediction accuracy, a
constructive algorithm is adopted in this paper to train the neural
network so that network weights and size are simultaneously
estimated. Then, a grid scheduler scheme is proposed to estimate
the queuing order that the tasks should be executed and the
most appopriate processor assignment so that the demanded
QoS are satisfied as much as possible. A fair scheduling policy is
considered as the most appropriate. Experimental results on a real
grid infrastructure are presented to illustrate the efficiency of the
proposed workload prediction — scheduling algorithm compared
to other approaches presented in the literature.
Abstract: The inference problem for propositional circumscription is known to
be highly intractable and, in fact, harder than the inference problem for classi-
cal propositional logic. More precisely, in its full generality this problem is P - 2
complete, which means that it has the same inherent computational complexity
as the satisfiability problem for quantified Boolean formulas with two alternations
(universal-existential) of quantifiers. We use Schaefer?s framework of generalized
satisfiability problems to study the family of all restricted cases of the inference
problem for propositional circumscription. Our main result yields a complete clas-
sification of the ?truly hard? ( P -complete) and the ?easier? cases of this problem
2
(reducible to the inference problem for classical propositional logic). Specifically,
we establish a dichotomy theorem which asserts that each such restricted case either
is P -complete or is in coNP. Moreover, we provide efficiently checkable criteria
2
that tell apart the ?truly hard? cases from the ?easier? ones. We show our results both
when the formulas involved are and are not allowed to contain constants. The present
work complements a recent paper by the same authors, where a complete classifi-
cation into hard and easy cases of the model-checking problem in circumscription
was established.
Abstract: We here present the Forward Planning Situated Protocol (FPSP), for scalable, energy efficient and fault tolerant data propagation in situated wireless sensor networks. To deal with the increased complexity of such deeply networked sensor systems, instead of emphasizing on a particular aspect of the services provided, i.e. either for low-energy periodic, or low-latency event-driven, or high-success query-based sensing, FPSP uses two novel mechanisms that allow the network operator to adjust the performance of the protocol in terms of energy, latency and success rate on a per-task basis. We emphasize on distributedness, direct or indirect interactions among relatively simple agents, flexibility and robustness.
The protocol operates by employing a series of plan & forward phases through which devices self-organize into forwarding groups that propagate data over discovered paths. FPSP performs a limited number of long range, high power data transmissions to collect information regarding the neighboring devices. The acquired information, allows to plan a (parameterizable long by {\"e}) sequence of short range, low power transmissions between nearby particles, based on certain optimization criteria. All particles that decide to respond (based on local criteria) to these long range transmissions enter the forwarding phase during which information is propagated via the acquired plan. Clearly, the duration of the forwarding phases is characterized by the parameter {\"e}, the transmission medium and the processing speed of the devices. In fact the parameter {\"e} provides a mechanism to adjust the protocol performance in terms of the latency--energy trade-off. By reducing {\"e} the latency is reduced at the cost of spending extra energy, while by increasing {\"e}, the energy dissipation is reduced but the latency is increased.
To control the success rate--energy trade-off, particles react locally on environment and context changes by using a set of rules that are based on response thresholds that relate individual-level plasticity with network-level resiliency, motivated by the nature-inspired method for dividing labor, a metaphor of social insect behavior for solving problems [1]. Each particle has an individual response threshold {\`E} that is related to the "local" density (as observed by the particle, [2]); particles engage in propagation of events when the level of the task-associated stimuli exceeds their thresholds. Let s be the intensity of a stimulus associated with a particular sensing task, set by the human authorities. We adopt the response function T{\`e}(s) = snover sn + {\`e}n, the probability of performing the task as a function of s, where n > 1 determines the steepness of the threshold. Thus, when {\`e} is small (i.e. the network is sparse) then the response probability increases; when s increases (i.e. for critical sensing tasks) the response probability increases as well.
This role-based approach where a selective number of devices do the high cost planning and the rest of the network operates in a low cost state leads to systems that have increased energy efficiency and high fault-tolerance since these long range planning phases allow to bypass obstacles (where no sensors are available) or faulty sensors (that have been disabled due to power failure or other natural events).
Abstract: This paper presents an overview of Quality of Service (QoS) differentiation mechanisms proposed for Optical Burst Switching (OBS) networks. OBS has been proposed to couple the benefits of both circuit and packet switching for the “on demand” use of capacity in the future optical Internet. In such a case, QoS support imposes some important challenges before this technology is deployed. This paper takes a broader view on QoS, including QoS differentiation not only at the burst but also at the transport levels for OBS networks. A classification of existing QoS differentiation mechanisms for OBS is given and their efficiency and complexity are comparatively discussed. We provide numerical examples on how QoS differentiation with respect to burst loss rate and transport layer throughput can be achieved in OBS networks.
Abstract: eVoting is a challenging approach for increasing eParticipation. However, lack of citizens¢ trust seems to be a main obstacle that hinders its successful realization. In this paper we propose a trust-centered engineering approach for building eVoting systems that people can trust, based on transparent design and implementation phases. The approach is based on three components: the decomposition of eVoting systems into “layers of trust” for reducing the complexity of managing trust issues in smaller manageable layers, the application of a risk analysis methodology able to identify and document security critical aspects of the eVoting system, and a cryptographically secure eVoting protocol. Our approach is pragmatic rather than theoretical in the sense that it sidesteps the controversy that besets the nature of trust in information systems and starts with a working definition of trust as people¢s positive attitude towards a system that performs its operations transparently.
Abstract: We discuss some new algorithmic and complexity issues in
coalitional and dynamic/evolutionary games, related to the understand-
ing of modern sel¯sh and Complex networks.
In particular: (a) We examine the achievement of equilibria via natural
distributed and greedy approaches in networks. (b) We present a model
of a coalitional game in order to capture the anarchy cost and complexity
of constructing equilibria in such situations. (c) We propose a stochastic
approach to some kinds of local interactions in networks, that can be
viewed also as extensions of the classical evolutionary game theoretic
setting.
Abstract: The 3-coloring problem is well known to be NP-complete. It is also well known that it
remains NP-complete when the input is restricted to graphs with diameter 4. Moreover, assuming
the Exponential Time Hypothesis (ETH), 3-coloring cannot be solved in time 2
o
(
n
)
on graphs with
n
vertices and diameter at most 4. In spite of the extensive studies of the 3-coloring problem with
respect to several basic parameters, the complexity status of this problem on graphs with small
diameter, i.e. with diameter at most 2, or at most 3, has been a longstanding and challenging open
question. In this paper we investigate graphs with small diameter. For graphs with diameter at most 2,
we provide the rst subexponential algorithm for 3-coloring, with complexity 2
O
(
p
n
log
n
)
, which is
asymptotically the same as the currently best known time complexity for the graph isomorphism
problem. Furthermore we extend the notion of an articulation vertex to that of an
articulation
neighborhood
, and we provide a polynomial algorithm for 3-coloring on graphs with diameter 2
that have at least one articulation neighborhood. For graphs with diameter at most 3, we establish
the complexity of 3-coloring, even for the case of triangle-free graphs. Namely we prove that for
every
"
2
[0
;
1), 3-coloring is NP-complete on triangle-free graphs of diameter 3 and radius 2 with
n
vertices and minimum degree
=
(
n
"
). Moreover, assuming ETH, we use three di erent ampli cation
techniques of our hardness results, in order to obtain for every
"
2
[0
;
1) subexponential asymptotic
lower bounds for the complexity of 3-coloring on triangle-free graphs with diameter 3 and minimum
degree
=
(
n
"
). Finally, we provide a 3-coloring algorithm with running time 2
O
(min
f
;
n
log
g
)
for
arbitrary graphs with diameter 3, where
n
is the number of vertices and
(resp.
) is the minimum
(resp. maximum) degree of the input graph. To the best of our knowledge, this algorithm is the rst
subexponential algorithm for graphs with
=
!
(1) and for graphs with
=
O
(1) and
=
o
(
n
).
Due to the above lower bounds of the complexity of 3-coloring, the running time of this algorithm is
asymptotically almost tight when the minimum degree of the input graph is
=
(
n
"
), where
"
2
[
1
2
;
1).
Abstract: In this paper we present a protocol for Certified E-Mail that ensures temporal authentication. We first slightly modify a previously known three-message optimistic protocol in order to obtain a building block that meets some properties. We then extend this basic protocol enhancing it with the temporal authentication by adding a single message, improving the message complexity of known protocols. The fairness of the protocol is ensured by an off-line Trusted third party that joins the protocol only in case one of the players misbehaves. In order to guarantee temporal authentication we assume the existance of an on-line time stamping server.
Abstract: This chapter is an introduction to the basic concepts and advances of a new field, that of Computational (or Algorithmic) Game Theory. We study the computational complexity of Nash equilibria and review the related algorithms proposed in the literature. Then, given the apparent difficulty of computing exact Nash equilibria, we study the efficient computation of approximate notions of Nash equilibria. Next we deal with several computational issues related to the class of congestion games, which model the selfish behavior of individuals when competing on the usage of a common set of resources. Finally, we study the price of anarchy (in the context of congestion games), which is defined as a measure of the performance degradation due to the the lack of coordination among the involved players.
Abstract: We study the partially eponymous model of distributed computation, which simultaneously
generalizes the anonymous and the eponymous models. In this model, processors have
identities, which are neither necessarily all identical (as in the anonymous model) nor
necessarily unique (as in the eponymous model). In a decision problem formalized as a
relation, processors receive inputs and seek to reach outputs respecting the relation. We
focus on the partially eponymous ring, and we shall consider the computation of circularly
symmetric relations on it. We consider sets of rings where all rings in the set have the same
multiset of identity multiplicities.
We distinguish between solvability and computability: in solvability, processors are
required to always reach outputs respecting the relation; in computability, they must
do so whenever this is possible, and must otherwise report impossibility.
We present a topological characterization of solvability for a relation on a set of rings,
which can be expressed as an efficiently checkable, number-theoretic predicate.
We present a universal distributed algorithm for computing a relation on a set of
rings; it runs any distributed algorithm for constructing views, followed by local steps.
We derive, as our main result, a universal upper bound on the message complexity to
compute a relation on a set of rings; this bound demonstrates a graceful degradation
with the Least Minimum Base, a parameter indicating the degree of least possible
eponymity for a set of rings. Thereafter, we identify two cases where a relation can be
computed on a set of rings, with rings of size n, with an efficient number of O .n lg n/
messages.
Abstract: In this paper, we present a Programmable Packet Processing Engine suitable for deep header processing in high-speed networking systems.
The engine, which has been – fabricated as part of a complete network processor, consists of a typical RISC-CPU, whose register
Wle has been modiWed in order to support eYcient context switching, and two simple special-purpose processing units. The engine can be
used in a number of network processing units (NPUs), as an alternative to the typical design practice of employing a large number of simple
general purpose processors, or in any other embedded system designed to process mainly network protocols. To assess the performance
of the engine, we have proWled typical networking applications and a series of experiments were carried out. Further, we have
compared the performance of our processing engine to that of two widely used NPUs and show that our proposed packet-processing
engine can run speciWc applications up to three times faster. Moreover, the engine is simpler to be fabricated, less complex in terms of
hardware complexity, while it can still be very easily programmed.
Abstract: Wireless Sensor Networks consist of a large number of small, autonomous devices, that are able to interact with their inveronment by sensing and collaborate to fulfill their tasks, as, usually, a single node is incapable of doing so; and they use wireless communication to enable this collaboration. Each device has limited computational and energy resources, thus a basic issue in the applicastions of wireless sensor networks is the low energy consumption and hence, the maximization of the network lifetime.
The collected data is disseminated to a static control point – data sink in the network, using node to node - multi-hop data propagation. However, sensor devices consume significant amounts of energy in addition to increased implementation complexity, since a routing protocol is executed. Also, a point of failure emerges in the area near the control center where nodes relay the data from nodes that are farther away. Recently, a new approach has been developed that shifts the burden from the sensor nodes to the sink. The main idea is that the sink has significant and easily replenishable energy reserves and can move inside the area the sensor network is deployed, in order to acquire the data collected by the sensor nodes at very low energy cost. However, the need to visit all the regions of the network may result in large delivery delays.
In this work we have developed protocols that control the movement of the sink in wireless sensor networks with non-uniform deployment of the sensor nodes, in order to succeed an efficient (with respect to both energy and latency) data collection. More specifically, a graph formation phase is executed by the sink during the initialization: the network area is partitioned in equal square regions, where the sink, pauses for a certain amount of time, during the network traversal, in order to collect data.
We propose two network traversal methods, a deterministic and a random one. When the sink moves in a random manner, the selection of the next area to visit is done in a biased random manner depending on the frequency of visits of its neighbor areas. Thus, less frequently visited areas are favored. Moreover, our method locally determines the stop time needed to serve each region with respect to some global network resources, such as the initial energy reserves of the nodes and the density of the region, stopping for a greater time interval at regions with higher density, and hence more traffic load. In this way, we achieve accelerated coverage of the network as well as fairness in the service time of each region.Besides randomized mobility, we also propose an optimized deterministic trajectory without visit overlaps, including direct (one-hop) sensor-to-sink data transmissions only.
We evaluate our methods via simulation, in diverse network settings and comparatively to related state of the art solutions. Our findings demonstrate significant latency and energy consumption improvements, compared to previous research.
Abstract: We here present Fun in Numbers (FinN), a framework for developing pervasive applications and interactive installations for entertainment and educational purposes. Using ad hoc mobile wireless sensor network nodes as the enabling devices, FinN allows for the quick prototyping of applications that utilize input from multiple physical sources (sensors and other means of interfacing), by o ffering a set of programming templates and services, such as topology discovery, localization and synchronization, that hide the underlying complexity. We present the target application domains of FinN, along with a set of multiplayer games and interactive installations. We describe the overall architecture of our platform
and discuss some key implementation issues of the application domains. Finally, we present the experience gained by deploying the applications developed with our platform.
Abstract: Direct routing is the special case of bufferless routing where N packets, once injected into the network, must be routed along specific paths to their destinations without conflicts. We give a general treatment of three facets of direct routing: (i) Algorithms. We present a polynomial time greedy algorithm for arbitrary direct routing problems whch is worst-case optimal, i.e., there exist instances for which no direct routing algorithm is better than the greedy. We apply variants of this algorithm to commonly used network topologies. In particular, we obtain near-optimal routing time using for the tree and d-dimensional mesh, given arbitrary sources and destinations; for the butterfly and the hypercube, the same result holds for random destinations. (ii) Complexity. By a reduction from Vertex Coloring, we show that Direct Routing is inapproximable, unless P=NP. (iii) Lower Bounds for Buffering. We show the existence of routing problems which cannot be solved efficiently with direct routing. To solve these problems, any routing algorithm needs buffers. We give nontrivial lower bounds on such buffering requirements for general routing algorithms.
Abstract: Two important performance parameters of distributed, rate-based flow control algorithms are their locality and convergence complexity. The former is characterized by the amount of global knowledge that is available to their scheduling mechanisms, while the latter is defined as the number of update operations performed on rates of individual sessions until max-min fairness is reached. Optimistic algorithms allow any session to intermediately receive a rate larger than its max-min fair rate; bottleneck algorithms finalize the rate of a session only if it is restricted by a certain, highly congested link of the network. In this work, we present a comprehensive collection of lower and upper bounds on convergence complexity, under varying degrees of locality, for optimistic, bottleneck, rate-based flow control algorithms. Say that an algorithm is oblivious if its scheduling mechanism uses no information of either the session rates or the network topology. We present a novel, combinatorial construction of a capacitated network, which we use to establish a fundamental lower bound of dn 4 + n 2 on the convergence complexity of any oblivious algorithm, where n is the number of sessions laid out on a network, and d, the session dependency, is a measure of topological dependencies among sessions. Moreover, we devise a novel simulation proof to establish that, perhaps surprisingly, the lower bound of dn 4 + n 2 on convergence complexity still holds for any partially oblivious algorithm, in which the scheduling mechanism is allowed to use information about session rates, but is otherwise unaware of network topology. On the positive side, we prove that the lower bounds for oblivious and partially oblivious algorithms are both tight. We do so by presenting optimal oblivious algorithms, which converge after dn 2 + n 2 update operations are performed in the worst case. To complete the picture, we show that linear convergence complexity can indeed be achieved if information about both session rates and network topology is available to schedulers. We present a counterexample, nonoblivious algorithm, which converges within an optimal number of n update operations. Our results imply a surprising convergence complexity collapse of oblivious and partially oblivious algorithms, and a convergence complexity separation between (partially) oblivious and nonoblivious algorithms for optimistic, bottleneck rate-based flow control.
Abstract: The problem of finding an implicit representation for a graph such that vertex adjacency can be tested quickly is fundamental to all graph algorithms. In particular, it is possible to represent sparse graphs on n vertices using O(n) space such that vertex adjacency is tested in O(l) time. We show here how to construct such a representation efficiently by providing simple and optimal algorithms, both in a sequential and a parallel setting. Our sequential algorithm runs in O(n) time. The parallel algorithm runs in O(log n) time using O(n/log n) CRCW PRAM processors, or inO(log n log* n) time using O(n/log n log* n) EREW PRAM processors. Previous results for this problem are based on matroid partitioning and thus have a high complexity.
Abstract: Intuitively, Braess's paradox states that destroying a part
of a network may improve the common latency of sel sh
ows at Nash
equilibrium. Such a paradox is a pervasive phenomenon in real-world
networks. Any administrator, who wants to improve equilibrium delays
in sel sh networks, is facing some basic questions: (i) Is the network
paradox-ridden? (ii) How can we delete some edges to optimize equilibrium
ow delays? (iii) How can we modify edge latencies to optimize
equilibrium
ow delays?
Unfortunately, such questions lead to NP-hard problems in general. In
this work, we impose some natural restrictions on our networks, e.g.
we assume strictly increasing linear latencies. Our target is to formulate
ecient algorithms for the three questions above.We manage to provide:
{ A polynomial-time algorithm that decides if a network is paradoxridden,
when latencies are linear and strictly increasing.
{ A reduction of the problem of deciding if a network with arbitrary
linear latencies is paradox-ridden to the problem of generating all
optimal basic feasible solutions of a Linear Program that describes
the optimal trac allocations to the edges with constant latency.
{ An algorithm for nding a subnetwork that is almost optimal wrt
equilibrium latency. Our algorithm is subexponential when the number
of paths is polynomial and each path is of polylogarithmic length.
{ A polynomial-time algorithm for the problem of nding the best
subnetwork, which outperforms any known approximation algorithm
for the case of strictly increasing linear latencies.
{ A polynomial-time method that turns the optimal
ow into a Nash
ow by deleting the edges not used by the optimal
ow, and performing
minimal modi cations to the latencies of the remaining ones.
Our results provide a deeper understanding of the computational complexity
of recognizing the Braess's paradox most severe manifestations,
and our techniques show novel ways of using the probabilistic method
and of exploiting convex separable quadratic programs.
Abstract: Intuitively, Braess’s paradox states that destroying a part of a network may improve the common latency of selfish flows at Nash equilibrium. Such a paradox is a pervasive phenomenon in real-world networks. Any administrator who wants to improve equilibrium delays in selfish networks, is facing some basic questions:
– Is the network paradox-ridden?
– How can we delete some edges to optimize equilibrium flow delays?
– How can we modify edge latencies to optimize equilibrium flow delays?
Unfortunately, such questions lead to View the MathML sourceNP-hard problems in general. In this work, we impose some natural restrictions on our networks, e.g. we assume strictly increasing linear latencies. Our target is to formulate efficient algorithms for the three questions above. We manage to provide:
– A polynomial-time algorithm that decides if a network is paradox-ridden, when latencies are linear and strictly increasing.
– A reduction of the problem of deciding if a network with (arbitrary) linear latencies is paradox-ridden to the problem of generating all optimal basic feasible solutions of a Linear Program that describes the optimal traffic allocations to the edges with constant latency.
– An algorithm for finding a subnetwork that is almost optimal wrt equilibrium latency. Our algorithm is subexponential when the number of paths is polynomial and each path is of polylogarithmic length.
– A polynomial-time algorithm for the problem of finding the best subnetwork which outperforms any known approximation for the case of strictly increasing linear latencies.
– A polynomial-time method that turns the optimal flow into a Nash flow by deleting the edges not used by the optimal flow, and performing minimal modifications on the latencies of the remaining ones.
Our results provide a deeper understanding of the computational complexity of recognizing the most severe manifestations of Braess’s paradox, and our techniques show novel ways of using the probabilistic method and of exploiting convex separable quadratic programs.
Abstract: In this work, we propose an energy-efficient multicasting algorithm
for wireless networks for the case where the transmission
powers of the nodes are fixed. Our algorithm is
based on the multicost approach and selects an optimal
energy-efficient set of nodes for multicasting, taking into account:
i) the node residual energies, ii) the transmission
powers used by the nodes, and iii) the set of nodes covered.
Our algorithm is optimal, in the sense that it can
optimize any desired function of the total power consumed
by the multicasting task and the minimum of the current
residual energies of the nodes, provided that the optimization
function is monotonic in each of these parameters. Our
optimal algorithm has non-polynomial complexity, thus, we
propose a relaxation producing a near-optimal solution in
polynomial time. The performance results obtained show
that the proposed algorithms outperform established solutions
for energy-aware multicasting, with respect to both
energy consumption and network lifetime. Moreover, it is
shown that the near-optimal multicost algorithm obtains
most of the performance benefits of the optimal multicost
algorithm at a smaller computational overhead.
Abstract: Evolutionary Game Theory is the study of strategic interactions
among large populations of agents who base their decisions on simple,
myopic rules. A major goal of the theory is to determine broad classes
of decision procedures which both provide plausible descriptions of selfish
behaviour and include appealing forms of aggregate behaviour. For example,
properties such as the correlation between strategies¢ growth rates
and payoffs, the connection between stationary states and the well-known
game theoretic notion of Nash equilibria, as well as global guarantees of
convergence to equilibrium, are widely studied in the literature.
Our paper can be seen as a quick introduction to Evolutionary Game
Theory, together with a new research result and a discussion of many
algorithmic and complexity open problems in the area. In particular, we
discuss some algorithmic and complexity aspects of the theory, which
we prefer to view more as Game Theoretic Aspects of Evolution rather
than as Evolutionary Game Theory, since the term “evolution” actually
refers to strategic adaptation of individuals¢ behaviour through a
dynamic process and not the traditional evolution of populations. We
consider this dynamic process as a self-organization procedure which,
under certain conditions, leads to some kind of stability and assures robustness
against invasion. In particular, we concentrate on the notion of
the Evolutionary Stable Strategies (ESS). We demonstrate their qualitative
difference from Nash Equilibria by showing that symmetric 2-person
games with random payoffs have on average exponentially less ESS than
Nash Equilibria. We conclude this article with some interesting areas of
future research concerning the synergy of Evolutionary Game Theory
and Algorithms.
Abstract: Online and Realtime counting and estimating the cardinality of sets is highly desirable for a large variety of applications, representing a foundational block for the efficient deployment and access of emerging internet scale information systems. In this work we implement three well known duplicate
insensitive counting algorithms and evaluate their performance in a testbed of resource-limited commercial off-the-shelf hardware devices. We focus on devices that can be used in wireless mobile and sensor applications and evaluate the memory complexity, time complexity and absolute error of the algorithms under different realistic scenaria. Our findings indicate the suitability of each algorithm depending on the application characteristics.
Abstract: We study the combinatorial structure and computational complexity of extreme Nash equilibria, ones that maximize or minimize a certain objective function, in the context of a selfish routing game. Specifically, we assume a collection of n users, each employing a mixed strategy, which is a probability distribution over m parallel links, to control the routing of its own assigned traffic. In a Nash equilibrium, each user routes its traffic on links that minimize its expected latency cost.
Our structural results provide substantial evidence for the Fully Mixed Nash Equilibrium Conjecture, which states that the worst Nash equilibrium is the fully mixed Nash equilibrium, where each user chooses each link with positive probability. Specifically, we prove that the Fully Mixed Nash Equilibrium Conjecture is valid for pure Nash equilibria and that under a certain condition, the social cost of any Nash equilibrium is within a factor of 6 + epsi, of that of the fully mixed Nash equilibrium, assuming that link capacities are identical.
Our complexity results include hardness, approximability and inapproximability ones. Here we show, that for identical link capacities and under a certain condition, there is a randomized, polynomial-time algorithm to approximate the worst social cost within a factor arbitrarily close to 6 + epsi. Furthermore, we prove that for any arbitrary integer k > 0, it is -hard to decide whether or not any given allocation of users to links can be transformed into a pure Nash equilibrium using at most k selfish steps. Assuming identical link capacities, we give a polynomial-time approximation scheme (PTAS) to approximate the best social cost over all pure Nash equilibria. Finally we prove, that it is -hard to approximate the worst social cost within a multiplicative factor . The quantity is the tight upper bound on the ratio of the worst social cost and the optimal cost in the model of identical capacities.
Abstract: The Internet and the Web have arguably surpassed the von Neumann Computer as the most complex computational artifacts of our times. Out of all the formidable characteristics of the Internet/Web, it seems that the most novel is its socio-economic complexity. The Internet and the Web are built, operated and used by a multitude of very diverse economic interests, which compete or collaborate in various degrees. In fact, this suggests that some very important insights about the Web may come from a fusion of ideas from Algorithms with concepts and techniques from Mathematical Economics and Game Theory. Since 2000, a new field has emerged (Algorithmic Game Theory and Computational Internet Economics), which examines exactly such ideas. We feel that this field belongs to Web Science. Some of the main topics of that field examined so far are Internet equilibria, the so called “Price of Anarchy” (a measure of loss of optimality due to selfishness [Koutsoupias,Papadimitriou (1999)], electronic markets and their equilibria, auctions, and algorithmic mechanisms design (inverse game theory or how to design a game in the net in such a clever way that individual players, motivated solely by their selfish interests, actually end up meeting the goals of the game designer!). Our paper here surveys the main concepts and results of this very promising subfield.
Abstract: We present improved methods for computing a set of alternative source-to-destination routes
in road networks in the form of an alternative graph. The resulting alternative graphs are
characterized by minimum path overlap, small stretch factor, as well as low size and complexity.
Our approach improves upon a previous one by introducing a new pruning stage preceding any
other heuristic method and by introducing a new filtering and fine-tuning of two existing methods.
Our accompanying experimental study shows that the entire alternative graph can be computed
pretty fast even in continental size networks.
Abstract: We present a new finger search tree with
O(
log log
d)
expected search time
in the Random Access Machine (RAM) model of computation for a large class of
input distributions. The parameter
d
represents the number of elements (distance) be-
tween the search element and an element pointed to by a finger, in a finger search tree
that stores
n
elements. Our data structure improves upon a previous result by Andersson and Mattsson that exhibits expected
O(
log log
n)
search time by incorporating the
distance
d
into the search time complexity, and thus removing the dependence on
n
.
We are also able to show that the search time is
O(
log log
d
+
φ(n))
with high prob-
ability, where
φ(n)
is
any
slowly growing function of
n
. For the need of the analysis
we model the updates by a “balls and bins” combinatorial game that is interesting in
its own right as it involves insertions and deletions of balls according to an unknown
distribution.
Abstract: We present a new finger search tree with O(log log d) expected search time in the Random
Access Machine (RAM) model of computation for a large class of input distributions. The
parameter d represents the number of elements (distance) between the search element and an
element pointed to by a finger, in a finger search tree that stores n elements. Our data structure
improves upon a previous result by Andersson and Mattsson that exhibits expected O(log log n)
search time by incorporating the distance d into the search time complexity, and thus removing
the dependence on n. We are also able to show that the search time is O(log log d + φ(n)) with
high probability, where φ(n) is any slowly growing function of n. For the need of the analysis
we model the updates by a “balls and bins” combinatorial game that is interesting in its own
right as it involves insertions and deletions of balls according to an unknown distribution.
Abstract: We propose efficient schemes for information-theoretically secure
key exchange in the Bounded Storage Model (BSM), where the adversary
is assumed to have limited storage. Our schemes generate a
secret One Time Pad (OTP) shared by the sender and the receiver,
from a large number of public random bits produced by the sender
or by an external source. Our schemes initially generate a small
number of shared secret bits, using known techniques. We introduce
a new method to expand a small number of shared bits to a
much longer, shared key.
Our schemes are tailored to the requirements of sensor nodes
and wireless networks. They are simple, efficient to implement and
take advantage of the fact that practical wireless protocols transmit
data in frames, unlike previous protocols, which assume access to
specific bits in a stream of data. Indeed, our main contribution is
twofold.
On the one hand, we construct schemes that are attractive in
terms of simplicity, computational complexity, number of bits read
from the shared random source and expansion factor of the initial
key to the final shared key.
On the other hand, we show how to transformany existing scheme
for key exchange in BSM into a more efficient scheme in the number
of bits it reads from the shared source, given that the source is
transmitted in frames.
Abstract: In this paper we present a multicost algorithm for the joint
time scheduling of the communication and computation
resources that will be used by a task. The proposed
algorithm selects the computation resource to execute the
task, determines the path to route the input data, and finds
the starting times for the data transmission and the task
execution, performing advance reservations. We initially
present an optimal scheme of non-polynomial complexity
and by appropriately pruning the set of candidate paths we
also give a heuristic algorithm of polynomial complexity. We
evaluate the performance of our algorithm and compare it to
that of algorithms that handle only the computation or
communication part of the problem separately. We show that
in a Grid network where the tasks are CPU- and dataintensive
important performance benefits can be obtained by
jointly optimizing the use of the communication and
computation resources.
Abstract: We consider Boolean formulas with three literals per clause,
or 3-SAT formulas. For random formulas with m clauses over n variables,
such as r = m=n is a constant, it has been experimentally observed
that, asymptotically as r crosses the threshold value 4:2 (approximately)
the probability that {\'A} is satis¯able falls abruptly from nearly 1 to 0.
Moreover, as n increases towards larger and larger values, the transition
of the probability becomes sharper. The purpose of this paper is to simply
outline a connection between the problem of determining bounds to the
threshold value and the concept of Kolmogorov complexity.
Abstract: We consider the problem of searching for a piece of
information in a fully interconnected computer network
(also called a complete network or clique) by exploiting
advice about its location from the network nodes. Each
node contains a database that ?knows? what kind of
documents or information are stored in other nodes
(e.g., a node could be a Web server that answers queries
about documents stored on the Web). The databases in
each node, when queried, provide a pointer that leads to
the node that contains the information. However, this
information is up-to-date (or correct) with some
bounded probability. While, in principle, one may always
locate the information by simply visiting the network
nodes in some prescribed ordering, this requires a time
complexity in the order of the number of nodes of the
network. In this paper, we provide algorithms for locating
an information node in the complete communication
network, which take advantage of advice given from
network nodes. The nodes may either give correct advice,
by pointing directly to the information node, or give
wrong advice, by pointing elsewhere. On the lowerbounds?
side, we show that no fixed-memory (i.e., with
memory independent of the network size) deterministic
algorithm may locate the information node in a constant
(independent of the network size) expected number of
steps. Moreover, if p (1/n) is the probability that a
node of an n-node clique gives correct advice, we show
that no algorithm may locate the information node in an
expected number of steps less than 1/p o(1). To study
how the expected number of steps is affected by the
amount of memory allowed to the algorithms, we give a
memoryless randomized algorithm with expected number
of steps 4/p o(1/p) o(1) and a 1-bit randomized
algorithm requiring on the average at most 2/p o(1)
steps. In addition, in the memoryless case, we also
prove a 4/p lower bound for the expected number of
steps in the case where the nodes giving faulty advice
may decide on the content of this advice in any possible
way and not merely at random (adversarial fault model).
Finally, for the case where faulty nodes behave randomly,
we give an optimal, unlimited memory deterministic
algorithm with expected number of steps bounded
from above by 1/p o(1/p) 1.
Abstract: We consider the problem of searching for a piece of information in a fully interconnected computer network or clique by exploiting
advice about its location from the network nodes Each node contains a
database that knows what kind of documents or information are stored
in other nodes e.g. a node could be a Web server that answers queries
about documents stored on the Web. The databases in each node when
queried provide a pointer that leads to the node that contains the information. However this information is up to date or correct with some
bounded probability. While in principle one may always locate the information by simply visiting the network nodes in some prescribed ordering
this requires a time complexity in the order of the number of nodes of the
network. In this paper we provide algorithms for locating an information node in the complete communication network that take advantage
of advice given from network nodes The nodes may either give correct
advice by pointing directly to the information node or give wrong advice
by pointing elsewhere We show that on the averageif the probability that a node provides correct advice is asymptotically larger than
where is the number of the computer nodes then the average time complexity for locating the information node is asymptotically or depending on the available memory.The probability may in general be a function of the number of network nodes . On the lower bounds
side we prove that noxed memory deterministic algorithm can locate
the information node in nite expected number of steps. We also prove
a lower bound of
for the expected number of steps of any algorithm
that locates the information node in the complete network.
Abstract: In this paper we propose an energy-aware broadcast algorithm for wireless networks. Our algorithm is based on the multicost approach and selects the set of nodes that by transmitting implement broadcasting in an optimally energy-efficient way. The energy-related parameters taken into account are the node transmission power and the node residual energy. The algorithm{\^a}€™s complexity however is non-polynomial, and therefore, we propose a relaxation producing a near-optimal solution in polynomial time. We also consider a distributed information exchange scheme that can be coupled with the proposed algorithms and examine the overhead introduced by this integration. Using simulations we show that the proposed algorithms outperform other solutions in the literature in terms of energy efficiency. Moreover, it is shown that the near-optimal algorithm obtains most of the performance benefits of the optimal algorithm at a smaller computational overhead.
Abstract: A key problem in Grid networks is how to efficiently manage the available infrastructure, in order to
satisfy user requirements and maximize resource utilization. This is in large part influenced by the
algorithms responsible for the routing of data and the scheduling of tasks. In this paper,wepresent several
multi-cost algorithms for the joint scheduling of the communication and computation resources that
will be used by a Grid task. We propose a multi-cost scheme of polynomial complexity that performs
immediate reservations and selects the computation resource to execute the task and determines the
path to route the input data. Furthermore, we introduce multi-cost algorithms that perform advance
reservations and thus also find the starting times for the data transmission and the task execution. We
initially present an optimal scheme of non-polynomial complexity and by appropriately pruning the set
of candidate paths we also give a heuristic algorithm of polynomial complexity. Our performance results
indicate that in a Grid network in which tasks are either CPU- or data-intensive (or both), it is beneficial
for the scheduling algorithm to jointly consider the computational and communication problems. A
comparison between immediate and advance reservation schemes shows the trade-offs with respect to
task blocking probability, end-to-end delay and the complexity of the algorithms.
Abstract: In this work, we showcase a set of implemented multiplayer games and interactive installations based on Fun in Numbers (FINN). FinN allows the quick prototyping of applications that utilize input from multiple physical sources (sensors and other means of interfacing), by offering a set of programming templates and services, such as proximity, localization and synchronization, that hide the underlying complexity.
Abstract: We study network load games, a class of routing games in
networks which generalize sel{\^A}¯sh routing games on networks consisting
of parallel links. In these games, each user aims to route some tra{\^A}±c from
a source to a destination so that the maximum load she experiences in the
links of the network she occupies is minimum given the routing decisions
of other users. We present results related to the existence, complexity,
and price of anarchy of Pure Nash Equilibria for several network load
games. As corollaries, we present interesting new statements related to
the complexity of computing equilibria for sel{\^A}¯sh routing games in net-
works of restricted parallel links.
Abstract: We study the fundamental problem 2NASH of computing a Nash equilibrium (NE) point in bimatrix games. We start by proposing a novel characterization of the NE set, via a bijective map to the solution set of a parameterized quadratic program (NEQP), whose feasible space is the highly structured set of correlated equilibria (CE). This is, to our knowledge, the first characterization of the subset of CE points that are in “1–1” correspondence with the NE set of the game, and contributes to the quite lively discussion on the relation between the spaces of CE and NE points in a bimatrix game (e.g., [15], [26] and [33]).
We proceed with studying a property of bimatrix games, which we call mutually concavity (MC), that assures polynomial-time tractability of 2NASH, due to the convexity of a proper parameterized quadratic program (either NEQP, or a parameterized variant of the Mangasarian & Stone formulation [23]) for a particular value of the parameter. We prove various characterizations of the MC-games, which eventually lead us to the conclusion that this class is equivalent to the class of strategically zero-sum (SZS) games of Moulin & Vial [25]. This gives an alternative explanation of the polynomial-time tractability of 2NASH for these games, not depending on the solvability of zero-sum games. Moreover, the recognition of the MC-property for an arbitrary game is much faster than the recognition SZS-property. This, along with the comparable time-complexity of linear programs and convex quadratic programs, leads us to a much faster algorithm for 2NASH in MC-games.
We conclude our discussion with a comparison of MC-games (or, SZS-games) to kk-rank games, which are known to admit for 2NASH a FPTAS when kk is fixed [18], and a polynomial-time algorithm for k=1k=1 [2]. We finally explore some closeness properties under well-known NE set preserving transformations of bimatrix games.
Abstract: A constraint network is arc consistent if any value of any of its variables is compatible with at
least one value of any other variable. The Arc Consistency Problem (ACP) consists in filtering out values of
the variables of a given network to obtain one that is arc consistent, without eliminating any solution. ACP is
known to be inherently sequential, or P-complete, so in this paper we examine some weaker versions of it and
their parallel complexity. We propose several natural approximation schemes for ACP and show that they are also
P-complete. In an attempt to overcome these negative results, we turn our attention to the problem of filtering
out values from the variables so that each value in the resulting network is compatible with at least one value of
not necessarily all, but a constant fraction of the other variables. We call such a network partially arc consistent.
We give a parallel algorithm that, for any constraint network, outputs a partially arc consistent subnetwork of it in
sublinear (O.pn log n/) parallel time using O.n2/ processors. This is the first (to our knowledge) sublinear-time
parallel algorithm with polynomially many processors that guarantees that in the resulting network every value is
compatible with at least one value in at least a constant fraction of the remaining variables. Finally, we generalize
the notion of partiality to the k-consistency problem.
Abstract: The voting rules proposed by Dodgson and Young are both
designed to nd the alternative closest to being a Condorcet
winner, according to two di erent notions of proximity; the
score of a given alternative is known to be hard to compute
under either rule.
In this paper, we put forward two algorithms for ap-
proximating the Dodgson score: an LP-based randomized
rounding algorithm and a deterministic greedy algorithm,
both of which yield an O(logm) approximation ratio, where
m is the number of alternatives; we observe that this result
is asymptotically optimal, and further prove that our greedy
algorithm is optimal up to a factor of 2, unless problems in
NP have quasi-polynomial time algorithms. Although the
greedy algorithm is computationally superior, we argue that
the randomized rounding algorithm has an advantage from
a social choice point of view.
Further, we demonstrate that computing any reasonable
approximation of the ranking produced by Dodgson's rule
is NP-hard. This result provides a complexity-theoretic
explanation of sharp discrepancies that have been observed
in the Social Choice Theory literature when comparing
Dodgson elections with simpler voting rules.
Finally, we show that the problem of calculating the
Young score is NP-hard to approximate by any factor. This
leads to an inapproximability result for the Young ranking.
Abstract: In routing games, the network performance at equilibrium can be significantly improved if we remove some edges from the network. This counterintuitive fact, widely known as Braess's paradox, gives rise to the (selfish) network design problem, where we seek to recognize routing games suffering from the paradox, and to improve the equilibrium performance by edge removal. In this work, we investigate the computational complexity and the approximability of the network design problem for non-atomic bottleneck routing games, where the individual cost of each player is the bottleneck cost of her path, and the social cost is the bottleneck cost of the network. We first show that bottleneck routing games do not suffer from Braess's paradox either if the network is series-parallel, or if we consider only subpath-optimal Nash flows. On the negative side, we prove that even for games with strictly increasing linear latencies, it is NP-hard not only to recognize instances suffering from the paradox, but also to distinguish between instances for which the Price of Anarchy (PoA) can decrease to 1 and instances for which the PoA is as large as \Omega(n^{0.121}) and cannot improve by edge removal. Thus, the network design problem for such games is NP-hard to approximate within a factor of O(n^{0.121-\eps}), for any constant \eps > 0. On the positive side, we show how to compute an almost optimal subnetwork w.r.t. the bottleneck cost of its worst Nash flow, when the worst Nash flow in the best subnetwork routes a non-negligible amount of flow on all used edges. The running time is determined by the total number of paths, and is quasipolynomial when the number of paths is quasipolynomial.
Abstract: In this paper we propose an energy-efficient broadcast algorithm for wireless networks for the case where the transmission powers of the nodes are fixed. Our algorithm is based on the multicost approach and selects an optimal energy-efficient set of nodes for broadcasting, taking into account: i) the node residual energies, ii) the transmission powers used by the nodes, and iii) the set of nodes that are covered by a specific schedule. Our algorithm is optimal, in the sense that it can optimize any desired function of the total power consumed by the broadcasting task and the minimum of the current residual energies of the nodes, provided that the optimization function is monotonic in each of these parameters. Our algorithm has non-polynomial complexity, thus, we propose a relaxation producing a near-optimal solution in polynomial time. Using simulations we show that the proposed algorithms outperform other established solutions for energy-aware broadcasting with respect to both energy consumption and network lifetime. Moreover, it is shown that the near-optimal multicost algorithm obtains most of the performance benefits of the optimal multicost algorithm at a smaller computational overhead.
Abstract: We propose a new theoretical model for passively mobile Wireless Sensor Networks. We
call it the PALOMA model, standing for PAssively mobile LOgarithmic space MAchines. The main
modification w.r.t. the Population Protocol model [2] is that agents now, instead of being automata, are
Turing Machines whose memory is logarithmic in the population size n. Note that the new model is still
easily implementable with current technology. We focus on complete communication graphs. We define
the complexity class PLM, consisting of all symmetric predicates on input assignments that are stably
computable by the PALOMA model. We assume that the agents are initially identical. Surprisingly, it
turns out that the PALOMA model can assign unique consecutive ids to the agents and inform them
of the population size! This allows us to give a direct simulation of a Deterministic Turing Machine
of O(n log n) space, thus, establishing that any symmetric predicate in SPACE(n log n) also belongs
to PLM. We next prove that the PALOMA model can simulate the Community Protocol model [15],
thus, improving the previous lower bound to all symmetric predicates in NSPACE(n log n). Going
one step further, we generalize the simulation of the deterministic TM to prove that the PALOMA
model can simulate a Nondeterministic TM of O(n log n) space. Although providing the same lower
bound, the important remark here is that the bound is now obtained in a direct manner, in the sense
that it does not depend on the simulation of a TM by a Pointer Machine. Finally, by showing that a
Nondeterministic TM of O(n log n) space decides any language stably computable by the PALOMA
model, we end up with an exact characterization for PLM: it is precisely the class of all symmetric
predicates in NSPACE(n log n).
Abstract: We propose a new theoretical model for passively mobile Wireless Sensor Networks, called PM, standing for Passively mobile Machines. The main modification w.r.t. the Population Protocol model [Angluin et al. 2006] is that agents now, instead of being automata, are Turing Machines. We provide general definitions for unbounded memories, but we are mainly interested in computations upper-bounded by plausible space limitations. However, we prove that our results hold for more general cases. We focus on \emph{complete interaction graphs} and define the complexity classes PMSPACE(f(n)) parametrically, consisting of all predicates that are stably computable by some PM protocol that uses O(f(n)) memory in each agent. We provide a protocol that generates unique identifiers from scratch only by using O(log n) memory, and use it to provide an exact characterization of the classes PMSPACE(f(n)) when f(n) = Ω(log n): they are precisely the classes of all symmetric predicates in NSPACE(nf(n)). As a consequence, we obtain a space hierarchy of the PM model when the memory bounds are Ω(log n). We next explore the computability of the PM model when the protocols use o(loglog n) space per machine and prove that SEM = PMSPACE(f(n)) when f(n) = o(loglog n), where SEM denotes the class of the semilinear predicates. Finally, we establish that the minimal space requirement for the computation of non-semilinear predicates is O(log log n).
Abstract: We propose a new theoretical model for passively mobile Wireless Sensor Networks, called PM, standing for Passively mobile Machines. The main modification w.r.t. the Population Protocol model [Angluin et al. 2006] is that the agents now, instead of being automata, are Turing Machines. We provide general definitions for unbounded memories, but we are mainly interested in computations upper-bounded by plausible space limitations. However, we prove that our results hold for more general cases. We focus on complete interaction graphs and define the complexity classes PMSPACE(f(n)) parametrically, consisting of all predicates that are stably computable by some PM protocol that uses O(f(n)) memory in each agent. We provide a protocol that generates unique identifiers from scratch only by using O(log n) memory, and use it to provide an exact characterization of the classes PMSPACE(f(n)) when f(n)=Omega(log n): they are precisely the classes of all symmetric predicates in NSPACE(nf(n)). As a consequence, we obtain a space hierarchy of the PM model when the memory bounds are Omega(log n). Finally, we establish that the minimal space requirement for the computation of non-semilinear predicates is O(log log n).
Abstract: In this paper we present an implementation and performance evaluation of a descent algorithm that was proposed in \cite{tsaspi} for the computation of approximate Nash equilibria of non-cooperative bi-matrix games. This algorithm, which achieves the best polynomially computable \epsilon-approximate equilibria till now, is applied here to several problem instances designed so as to avoid the existence of easy solutions. Its performance is analyzed in terms of quality of approximation and speed of convergence. The results demonstrate significantly better performance than the theoretical worst case bounds, both for the quality of approximation and for the speed of convergence. This motivates further investigation into the intrinsic characteristics of descent algorithms applied to bi-matrix games. We discuss these issues and provide some insights about possible variations and extensions of the algorithmic concept that could lead to further understanding of the complexity of computing equilibria. We also prove here a new significantly better bound on the number of loops required for convergence of the descent algorithm.
Abstract: In this paper we study the problem of assigning transmission ranges to the nodes of a multihop
packet radio network so as to minimize the total power consumed under the constraint
that adequate power is provided to the nodes to ensure that the network is strongly connected
(i.e., each node can communicate along some path in the network to every other node). Such
assignment of transmission ranges is called complete. We also consider the problem of achieving
strongly connected bounded diameter networks.
For the case of n + 1 colinear points at unit distance apart (the unit chain) we give a tight
asymptotic bound for the minimum cost of a range assignment of diameter h when h is a xed
constant and when h>(1 + ) log n, for some constant > 0. When the distances between the
colinear points are arbitrary, we give an O(n4) time dynamic programming algorithm for nding
a minimum cost complete range assignment.
For points in three dimensions we show that the problem of deciding whether a complete
range assignment of a given cost exists, is NP-hard. For the same problem we give an O(n2)
time approximation algorithm which provides a complete range assignment with cost within a
factor of two of the minimum. The complexity of this problem in two dimensions remains open,
while the approximation algorithm works in this case as well.
Abstract: Wireless sensor and actor networks are comprised of a large number of small, fully autonomous computing, communication, sensing and actuation devices, with very restricted energy and computing capabilities. Such devices co-operate to accomplish a large sensing and acting task. Sensors gather information for an event in the physical world and notify the actors that perform appropriate actions by making a decision on receipt of the sensed information. Such networks can be very useful in practice i.e.~in the local detection of remote crucial events and the propagation of relevant data to decision
centers that perform appropriate actions upon the environment, thus realizing sensing and acting from a distance.
In this work we present a communication protocol that enables scalable, energy efficient and fault tolerant coordination while allowing to prioritize sensing tasks in situated wireless sensor and actor networks. The sensors react locally on environment and context changes and interact with each other in order to adjust the performance of the network in terms of energy, latency and success rate on a per-task basis. To deal with the increased complexity of such large-scale systems, our protocol pulls some additional knowledge about the network in order to subsequently improve data forwarding towards the actors.
We implement and evaluate the protocol using large scale simulation, showing its suitability in networks where sensor to actor and actor to actor coordination are important for accomplishing tasks of different priorities.
Abstract: The sensor devices are battery powered thus energy is the most precious resource of a wireless sensor
network since periodically replacing the battery of the nodes in large scale deployments is infeasible. The
collected data is disseminated to a static control point { data sink in the network, using node to node
{ multi-hop data propagation, [4, 6]. However, sensor devices consume signi cant amounts of energy in
addition to increased implementation complexity since a routing protocol is executed. Also, a point of
failure emerges in the area near the control center where nodes relay the data from nodes that are farther
away
Abstract: In recent years there has been signi1cant interest in the study of random k-SAT formulae. For
a given set of n Boolean variables, let Bk denote the set of all possible disjunctions of k distinct,
non-complementary literals from its variables (k-clauses). A random k-SAT formula Fk (n;m) is
formed by selectinguniformly and independently m clauses from Bk and takingtheir conjunction.
Motivated by insights from statistical mechanics that suggest a possible relationship between the
?order? of phase transitions and computational complexity, Monasson and Zecchina (Phys. Rev.
E 56(2) (1997) 1357) proposed the random (2+p)-SAT model: for a given p ¸ [0; 1], a random
(2 + p)-SAT formula, F2+p(n;m), has m randomly chosen clauses over n variables, where pm
clauses are chosen from B3 and (1 − p)m from B2. Usingthe heuristic ?replica method? of
statistical mechanics, Monasson and Zecchina gave a number of non-rigorous predictions on the
behavior of random (2 + p)-SAT formulae. In this paper we give the 1rst rigorous results for
random (2 + p)-SAT, includingthe followingsurprisingfact: for p 6 2=5, with probability
1 − o(1), a random (2 + p)-SAT formula is satis1able i@ its 2-SAT subformula is satis1able.
That is, for p 6 2=5, random (2 + p)-SAT behaves like random 2-SAT.
Abstract: A key problem in networks that support advance reservations is the routing and time scheduling of connections with flexible starting time and known data transfer size. In this paper we present a multicost routing and scheduling algorithm for selecting the path to be followed by such a connection and the time the data should start and end transmission at each link so as to minimize the reception time at the destination, or optimize some other performance criterion. The utilization profiles of the network links, the link propagation delays, and the parameters of the connection to be scheduled form the inputs to the algorithm. We initially present a scheme of non-polynomial complexity to compute a set of so called non-dominated candidate paths, from which the optimal path can be found. We then propose two mechanisms to appropriately prune the set of candidate paths in order to find multicost routing and scheduling algorithms of polynomial complexity. We examine the performance of the algorithms in the special case of an Optical Burst Switched network. Our results indicate that the proposed polynomial-time algorithms have performance that is very close to that of the optimal algorithm. We also study the effects network propagation delays and link-state update policies have on performance.
Abstract: A key problem in networks that support advance reservations is the routing and time scheduling of
connections with flexible starting time and known data transfer size. In this paper we present a multicost
routing and scheduling algorithm for selecting the path to be followed by such a connection and the time the
data should start and end transmission at each link so as to minimize the reception time at the destination,
or optimize some other performance criterion. The utilization profiles of the network links, the link
propagation delays, and the parameters of the connection to be scheduled form the inputs to the algorithm.
We initially present a scheme of non-polynomial complexity to compute a set of so-called non-dominated
candidate paths, from which the optimal path can be found. We then propose two mechanisms to
appropriately prune the set of candidate paths in order to find multicost routing and scheduling algorithms of
polynomial complexity. We examine the performance of the algorithms in the special case of an Optical
Burst Switched network. Our results indicate that the proposed polynomial time algorithms have performance that is very close to that of the optimal algorithm. We also study the effects network
propagation delays and link-state update policies have on performance.
Abstract: A key problem in networks that support advance
reservations is the routing and time scheduling of connections
with flexible starting time. In this paper we present a multicost
routing and scheduling algorithm for selecting the path to be
followed by such a connection and the time the data should start
so as to minimize the reception time at the destination, or some
other QoS requirement. The utilization profiles of the network
links, the link propagation delays, and the parameters of the
connection to be scheduled form the inputs to the algorithm. We
initially present a scheme of non-polynomial complexity to
compute a set of so-called non-dominated candidate paths, from
which the optimal path can be found. By appropriately pruning
the set of candidate paths using path pseudo-domination
relationships, we also find multicost routing and scheduling
algorithms of polynomial complexity. We examine the
performance of the algorithms in the special case of an Optical
Burst Switched network. Our results indicate that the proposed
polynomial time algorithms have performance that it is very close
to that of the optimal algorithm.
Abstract: In 1876 Charles Lutwidge Dodgson suggested the intriguing voting rule that today bears his name. Although Dodgson's rule is one of the most well-studied voting rules, it suffers from serious de ciencies, both from the computational point of view|it is NP-hard even to approximate the Dodgson score within sublogarithmic factors|and from the social choice point of view|it fails basic social choice desiderata such as monotonicity and homogeneity.
In a previous paper [Caragiannis et al., SODA 2009] we have asked whether there are approximation algorithms for Dodgson's rule that are monotonic or homogeneous. In this paper we give de nitive answers to these questions. We design a monotonic exponential-time algorithm that yields a 2-approximation to the Dodgson score, while matching this result with a tight lower bound. We also present a monotonic polynomial-time O(logm)-approximation algorithm (where m is the number of alternatives); this result is tight as well due to a complexity-theoretic lower bound. Furthermore, we show that a slight variation of a known voting rule yields a monotonic, homogeneous, polynomial-time O(mlogm)-approximation algorithm, and establish that it is impossible to achieve a better approximation ratio even if one just asks for homogeneity. We complete the picture by studying several additional social choice properties; for these properties, we prove that algorithms with an approximation ratio that depends only on m do not exist.
Abstract: In 1876 Charles Lutwidge Dodgson suggested the intriguing
voting rule that today bears his name. Although Dodg-
son's rule is one of the most well-studied voting rules, it suf-
fers from serious de ciencies, both from the computational
point of view|it is NP-hard even to approximate the Dodg-
son score within sublogarithmic factors|and from the social
choice point of view|it fails basic social choice desiderata
such as monotonicity and homogeneity.
In a previous paper [Caragiannis et al., SODA 2009] we
have asked whether there are approximation algorithms for
Dodgson's rule that are monotonic or homogeneous. In this
paper we give de nitive answers to these questions. We de-
sign a monotonic exponential-time algorithm that yields a
2-approximation to the Dodgson score, while matching this
result with a tight lower bound. We also present a monotonic
polynomial-time O(logm)-approximation algorithm (where
m is the number of alternatives); this result is tight as well
due to a complexity-theoretic lower bound. Furthermore,
we show that a slight variation of a known voting rule yields
a monotonic, homogeneous, polynomial-time O(mlogm)-
approximation algorithm, and establish that it is impossible
to achieve a better approximation ratio even if one just asks
for homogeneity. We complete the picture by studying sev-
eral additional social choice properties; for these properties,
we prove that algorithms with an approximation ratio that
depends only on m do not exist.
Abstract: In emerging pervasive scenarios, data is collected by sensing devices in streams that occur at several distributed points of observation. The size of the data typically far exceeds the storage and computational capabilities of the tiny devices that have to collect and process them. A general and challenging task is to allow (some of) the nodes of a pervasive network to collectively perform monitoring of a neighbourhood of interest by issuing continuous aggregate queries on the streams observed in its vicinity. This class of algorithms is fully decentralized and diffusive in nature: collecting all the data at a few central nodes of the network is unfeasible in networks of low capability devices or in the presence of massive data sets. Two main problems arise in this scenario: (i) the intrinsic complexity of maintaining statistics over a data stream whose size greatly exceeds the capabilities of the device that performs the computation; (ii) composing the partial outcomes computed at different points of observation into an accurate, global statistic over a neighbourhood of interest, which entails coping with several problems, last but not least the receipt of duplicate information along multiple paths of diffusion.
Streaming techniques have emerged as powerful tools to achieve the general goals described above, in the first place because they assume a computational model in which computational and storage resources are assumed to be far exceeded by the amount of data on which computation occurs. In this contribution, we review the main streaming techniques and provide a classification of the computational problems and the applications they effectively address, with an emphasis on decentralized scenarios, which are of particular interest in pervasive networks
Abstract: A dichotomy theorem for a class of decision problems is a result asserting that certain problems in the
class are solvable in polynomial time, while the rest are NP-complete. The first remarkable such dichotomy
theorem was proved by Schaefer in 1978. It concerns the class of generalized satisfiability problems Sat?S{\L},
whose input is a CNF?S{\L}-formula, i.e., a formula constructed from elements of a fixed set S of generalized
connectives using conjunctions and substitutions by variables. Here, we investigate the complexity of
minimal satisfiability problems Min Sat?S{\L}, where S is a fixed set of generalized connectives. The input to
such a problem is a CNF?S{\L}-formula and a satisfying truth assignment; the question is to decide whether
there is another satisfying truth assignment that is strictly smaller than the given truth assignment with
respect to the coordinate-wise partial order on truth assignments. Minimal satisfiability problems were first
studied by researchers in artificial intelligence while investigating the computational complexity of prop-
ositional circumscription. The question of whether dichotomy theorems can be proved for these problems
was raised at that time, but was left open. We settle this question affirmatively by establishing a dichotomy
theorem for the class of all Min Sat?S{\L}-problems, where S is a finite set of generalized connectives. We also
prove a dichotomy theorem for a variant of Min Sat?S{\L} in which the minimization is restricted to a subset of
the variables, whereas the remaining variables may vary arbitrarily (this variant is related to extensions of
propositional circumscription and was first studied by Cadoli). Moreover, we show that similar dichotomy
theorems hold also when some of the variables are assigned constant values. Finally, we give simple criteria that tell apart the polynomial-time solvable cases of these minimal satisfiability problems from the NP-
complete ones.
Abstract: We consider a security problem on a distributed network.
We assume a network whose nodes are vulnerable to infection
by threats (e.g. viruses), the attackers. A system security
software, the defender, is available in the system. However,
due to the network¢s size, economic and performance reasons,
it is capable to provide safety, i.e. clean nodes from
the possible presence of attackers, only to a limited part of
it. The objective of the defender is to place itself in such a
way as to maximize the number of attackers caught, while
each attacker aims not to be caught.
In [7], a basic case of this problem was modeled as a
non-cooperative game, called the Edge model. There, the
defender could protect a single link of the network. Here,
we consider a more general case of the problem where the
defender is able to scan and protect a set of k links of the
network, which we call the Tuple model. It is natural to expect
that this increased power of the defender should result
in a better quality of protection for the network. Ideally,
this would be achieved at little expense on the existence and
complexity of Nash equilibria (profiles where no entity can
improve its local objective unilaterally by switching placements
on the network).
In this paper we study pure and mixed Nash equilibria
in the model. In particular, we propose algorithms for computing
such equilibria in polynomial time and we provide a
polynomial-time transformation of a special class of Nash
equilibria, called matching equilibria, between the Edge
model and the Tuple model, and vice versa. Finally, we
establish that the increased power of the defender results in
higher-quality protection of the network.
Abstract: Let M be a single s-t network of parallel links with load dependent latency functions shared by an infinite number of selfish users. This may yield a Nash equilibrium with unbounded Coordination Ratio [E. Koutsoupias, C. Papadimitriou, Worst-case equilibria, in: 16th Annual Symposium on Theoretical Aspects of Computer Science, STACS, vol. 1563, 1999, pp. 404-413; T. Roughgarden, E. Tardos, How bad is selfish routing? in: 41st IEEE Annual Symposium of Foundations of Computer Science, FOCS, 2000, pp. 93-102]. A Leader can decrease the coordination ratio by assigning flow {\'a}r on M, and then all Followers assign selfishly the (1-{\'a})r remaining flow. This is a Stackelberg Scheduling Instance(M,r,{\'a}),0≤{\'a}≤1. It was shown [T. Roughgarden, Stackelberg scheduling strategies, in: 33rd Annual Symposium on Theory of Computing, STOC, 2001, pp. 104-113] that it is weakly NP-hard to compute the optimal Leader's strategy. For any such network M we efficiently compute the minimum portion @b"M of flow r>0 needed by a Leader to induce M's optimum cost, as well as her optimal strategy. This shows that the optimal Leader's strategy on instances (M,r,@a>=@b"M) is in P. Unfortunately, Stackelberg routing in more general nets can be arbitrarily hard. Roughgarden presented a modification of Braess's Paradox graph, such that no strategy controlling {\'a}r flow can induce ≤1/{\'a} times the optimum cost. However, we show that our main result also applies to any s-t net G. We take care of the Braess's graph explicitly, as a convincing example. Finally, we extend this result to k commodities. A conference version of this paper has appeared in [A. Kaporis, P. Spirakis, The price of optimum in stackelberg games on arbitrary single commodity networks and latency functions, in: 18th annual ACM symposium on Parallelism in Algorithms and Architectures, SPAA, 2006, pp. 19-28]. Some preliminary results have also appeared as technical report in [A.C. Kaporis, E. Politopoulou, P.G. Spirakis, The price of optimum in stackelberg games, in: Electronic Colloquium on Computational Complexity, ECCC, (056), 2005].
Abstract: One of the most challenging problems in probability and complexity theory is
to establish and determine the satisfiability threshold, or phase transition, for
random k-SAT instances: Boolean formulas consisting of clauses with exactly k
literals. As the previous part of the volume has explored, empirical observations
suggest that there exists a critical ratio of the number of clauses to the number
of variables, such that almost all randomly generated formulas with a higher
ratio are unsatisfiable while almost all randomly generated formulas with a lower
ratio are satisfiable. The statement that such a crossover point really exists is
called the satisfiability threshold conjecture. Experiments hint at such a direction,
but as far as theoretical work is concerned, progress has been difficult. In an
important advance, Friedgut [23] showed that the phase transition is a sharp one,
though without proving that it takes place at a “fixed” ratio for large formulas.
Otherwise, rigorous proofs have focused on providing successively better upper
and lower bounds for the value of the (conjectured) threshold. In this chapter, our
Abstract: In this work, we study the combinatorial structure and the
computational complexity of Nash equilibria for a certain game that
models selfish routing over a network consisting of m parallel links. We
assume a collection of n users, each employing a mixed strategy, which
is a probability distribution over links, to control the routing of its own
assigned traffic. In a Nash equilibrium, each user selfishly routes its traffic
on those links that minimize its expected latency cost, given the network
congestion caused by the other users. The social cost of a Nash equilibrium
is the expectation, over all random choices of the users, of the
maximum, over all links, latency through a link.
We embark on a systematic study of several algorithmic problems related
to the computation of Nash equilibria for the selfish routing game we consider.
In a nutshell, these problems relate to deciding the existence of a
Nash equilibrium, constructing a Nash equilibrium with given support
characteristics, constructing the worst Nash equilibrium (the one with
maximum social cost), constructing the best Nash equilibrium (the one
with minimum social cost), or computing the social cost of a (given) Nash
equilibrium. Our work provides a comprehensive collection of efficient algorithms,
hardness results (both as NP-hardness and #P-completeness
results), and structural results for these algorithmic problems. Our results
span and contrast a wide range of assumptions on the syntax of the
Nash equilibria and on the parameters of the system.
Abstract: In this paper we study the threshold behavior of the fixed radius random graph model and its applications to the key management problem of sensor networks and, generally, for mobile ad-hoc networks. We show that this random graph model can realistically model the placement of nodes within a certain region and their interaction/sensing capabilities (i.e. transmission range, light sensing sensitivity etc.). We also show that this model can be used to define key sets for the network nodes that satisfy a number of good properties, allowing to set up secure communication with each other depending on randomly created sets of keys related to their current location. Our work hopes to inaugurate a study of key management schemes whose properties are related to properties of an appropriate random graph model and, thus, use the rich theory developed in the random graph literature in order to transfer ?good? properties of the graph model to the key sets of the nodes.
Partially supported by the IST Programme of the European Union under contact number IST-2005-15964 (AEOLUS) and the INTAS Programme under contract with Ref. No 04-77-7173 (Data Flow Systems: Algorithms and Complexity (DFS-AC)).
