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: 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: 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: 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: 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: 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 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: 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 complexityclass 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 complexityclasses 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 complexityclasses 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 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.
