Abstract: Consider a network vulnerable to viral infection. The system security software can guarantee
safety only to a limited part of the network. Such limitations result from economy costs or processing
costs. The problem raised is to which part of the network the security software should
be installed, so that to secure as much as possible the network. We model this practical network
scenario as a non-cooperative multi-player game on a graph, with two kinds of players, a set
of attackers and a protector player, representing the viruses and the system security software,
respectively. Each attacker player chooses a node of the graph (or a set of them, via a probability
distribution) to infect. The protector player chooses independently, in a basic case of the
problem, a simple path or an edge of the graph (or a set of them, via a probability distribution)
and cleans this part of the network from attackers. Each attacker wishes to maximize the probability
of escaping its cleaning by the protector. In contrast, the protector aims at maximizing
the expected number of cleaned attackers. We call the two games obtained from the two basic
cases considered, as the Path and the Edge model, respectively. For these two games, we are
interested in the associated Nash equilibria, where no network entity can unilaterally improve
its local objective. We obtain the following results:
• The problem of existence of a pure Nash equilibrium is NP-complete for the Path model.
This opposed to that, no instance of the Edge model possesses a pure Nash equilibrium,
proved in [7].
• In [7] a characterization of mixed Nash equilibria for the Edge model is provided. However,
that characterization only implies an exponential time algorithm for the general case.
Here, combining it with clever exploration of properties of various practical families of
graphs, we compute, in polynomial time, mixed Nash equilibria on corresponding graph
instances. These graph families include, regular graphs, graphs that can be decomposed, in
polynomially time, into vertex disjoint r-regular subgraphs, graphs with perfect matchings
and trees.
• We utilize the notion of social cost [6] for measuring system performance on such scenario;
here is defined to be the utility of the protector. We prove that the corresponding Price of
Anarchy in any mixed Nash equilibria of the game is upper and lower bounded by a linear
function of the number of vertices of the graph.

Abstract: Consider a network vulnerable to viral infection, where the security software can guarantee safety only to a limited part of it. We model this practical network scenario as a non-cooperative multi-player game on a graph, with two kinds of players, a set of attackers and a protector player, representing the viruses and the system security software, respectively. We are interested in the associated Nash equilibria, where no network entity can unilaterally improve its local objective. We obtain the following results: for certain families of graphs, mixed Nash equilibria can be computed in polynomially time. These families include, among others, regular graphs, graphs with perfect matchings and trees. The corresponding price of anarchy for any mixed Nash equilibria of the game is upper and lower bounded by a linear function of the number of vertices of the graph. (We define the price of anarchy to reflect the utility of the protector). Finally, we introduce a generalised version of the game. We show that the existence problem of pure Nash equilibria here is NP complete.

Abstract: Wireless Sensor Networks are by nature highly dynamic and communication between sensors is completely ad hoc, especially when mobile devices are part of the setup. Numerous protocols and applications proposed for such networks
operate on the assumption that knowledge of the neighborhood is a priori available to all nodes. As a result, WSN deployments need to use or implement from scratch a neighborhood discovery mechanism. In this work we present a new protocol based on adaptive periodic beacon exchanges. We totally avoid continuous beaconing by adjusting the rate of broadcasts using the concept of consistency over the understanding of neighborhood that nearby devices share. We propose, implement and evaluate our adaptive neighborhood discovery protocol over our experimental testbed and using large scale simulations. Our results indicate that the
new protocol operates more eciently than existing reference implementations while it provides valid information to applications that use it. Extensive performance evaluation indicates that it successfully reduces generated network traffic by 90% and increases network lifetime by 20% compared to existing mechanisms that rely on continuous beaconing.

Abstract: We propose and evaluate fast reservation (FR)
protocols for Optical Burst Switched (OBS) networks. The
proposed reservation schemes aim at reducing the end-to-end
delay of a data burst, by sending the Burst Header Packet (BHP)
in the core network before the burst assembly is completed at the
ingress node. We use linear prediction filters to estimate the
expected length of the burst and the time needed for the
burstification process to complete. A BHP packet carrying these
estimates is sent before burst completion, in order to reserve
bandwidth at each intermediate node for the time interval the
burst is expected to pass from that node. Reducing the total time
needed for a packet to be transported over an OBS network is
important, especially for real-time applications. Reserving
bandwidth only for the time interval it is actual going to be used
by a burst is important for network utilization efficiency. In the
simulations conducted we evaluate the proposed extensions and
prove their usefulness.

Abstract: We study the problem of maintaining connectivity in a wireless
network where the network nodes are equipped with
directional antennas. Nodes correspond to points on the
plane and each uses a directional antenna modeled by a sector
with a given angle and radius. The connectivity problem
is to decide whether or not it is possible to orient the antennas
so that the directed graph induced by the node transmissions
is strongly connected. We present algorithms for
simple polynomial-time-solvable cases of the problem, show
that the problem is NP-complete in the 2-dimensional case
when the sector angle is small, and present algorithms that
approximate the minimum radius to achieve connectivity for
sectors with a given angle. We also discuss several extensions
to related problems. To the best of our knowledge, the
problem has not been studied before in the literature.

Abstract: In this article, we present a detailed performance
evaluation of a hybrid optical switching (HOS)
architecture called Overspill Routing in Optical Networks
(ORION). The ORION architecture combines
(optical) wavelength and (electronic) packet switching,
so as to obtain the individual advantages of both switching
paradigms. In particular, ORION exploits the possible insertions/extractions, to reduce the necessary
interfaces, do not deteriorate performance and thus the
use of traffic concentrators assure ORION’s economic
viability.
idle periods of established lightpaths to transmit
packets destined to the next common node, or even
directly to their common end-destination. Depending
on whether all lightpaths are allowed to simultaneously
carry and terminate overspill traffic or overspill is restricted
to a sub-set of wavelengths, the architecture
limits itself to constrained or un-constrained ORION. To
evaluate both cases, we developed an extensive network
simulator where the basic features of the ORION architectureweremodeled,
including suitable edge/core node
switches and load-varying sources to simulate overloading
traffic conditions. Further, we have assessed various
aspects of the ORION architecture including two
basic routing/forwarding policies and various buffering
schemes. The completenetwork study shows that
ORION can absorb temporal traffic overloads, as intended,
provided sufficient buffering is present.We also
demonstrate that the restriction of simultaneous packet

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 completenetwork 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: 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: Orthogonal Frequency Division Multiplexing (OFDM)
has recently been proposed as a modulation technique for optical networks, because of its good spectral efficiency, flexibility, and tolerance to impairments. We consider the planning problem of an OFDM optical network, where we are given a traffic matrix that includes the requested transmission rates of the connections to be served. Connections are provisioned for their requested rate by elastically allocating spectrum using a variable number of OFDM subcarriers and choosing an appropriate modulation level, taking into account the transmission distance. We introduce the Routing, Modulation Level and Spectrum Allocation (RMLSA) problem, as opposed to the typical Routing and Wavelength Assignment (RWA) problem of traditional WDM networks, prove that is also NP-complete and present various algorithms to solve it. We start by presenting an optimal ILP RMLSA algorithm that minimizes the spectrum used to serve the traffic matrix, and also present a decomposition method that breaks RMLSA into its two
substituent subproblems, namely, (i) routing and modulation level, and (ii) spectrum allocation (RML+SA), and solves them sequentially. We also propose a heuristic algorithm that serves connections one-by-one and use it to solve the planning problem by sequentially serving all the connections in the traffic matrix. In the sequential algorithm, we investigate two policies for defining the order in which connections are considered. We also use a simulated annealing meta-heuristic to obtain even better orderings. We examine the performance of the proposed algorithms through simulation experiments and evaluate the spectrum utilization benefits that can be obtained by utilizing OFDM elastic bandwidth allocation, when compared to a traditional WDM network.

Abstract: We study the problem of fair resource allocation in a simple cooperative multi-agent setting where we have k agents and a set of n objects to be allocated to those agents. Each object is associated with a weight represented by a positive integer or real number. We would like to allocate all objects to the agents so that each object is allocated to only one agent and the weight is distributed fairly. We adopt the fairness index popularized by the networking community as our measure of fairness, and study centralized algorithms for fair resource allocation. Based on the relationship between our problem and number partitioning, we devise a greedy algorithm for fair resource allocation that runs in polynomial time but is not guaranteed to find the optimal solution, and a complete anytime algorithm that finds the optimal solution but runs in exponential time. Then we study the phase transition behavior of the complete algorithm. Finally, we demonstrate that the greedy algorithm actually performs very well and returns almost perfectly fair allocations.

Abstract: We consider the problem of searching for a piece of
information in a fully interconnected computer network
(also called a completenetwork 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 completenetwork.

Abstract: Flow control is the main technique currently used to prevent some of the ordered traffic from entering a communication network, and to avoid congestion. A challenging aspect of flow control is how to treat all sessions "fairly " when it is necessary to turn traffic away from the network. In this work, we show how to extend the theory of max-min fair flow control to the case where priorities are assigned to different varieties of traffic, which are sensitive to traffic levels. We examine priorities expressible in the general form of increasing functions of rates, considering yet in combination the more elaborative case with unescapable upper and lower bounds on rates of traffic sessions. We offer optimal, priority bottleneck algorithms, which iteratively adjust the session rates in order to meet a new condition of max-min fairness under priorities and rate bounds. In our setting, which is realistic for today's technology of guaranteed quality of service, traffic may be turned away not only to avoid congestion, but also to respect particular minimum requirements on bandwidth. Moreover, we establish lower bounds on the competitiveness of network-oblivious schemes compared to optimal schemes with complete knowledge of network structure. Our theory extends significantly the classical theory of max-min fair flow control [2]. Moreover, our results on rejected traffic are fundamentally different from those related to call control and bandwidth allocation, since not only do we wish to optimize the number and rates of accepted sessions, but we also require priority fairness.

Abstract: We extend here the Population Protocol model of Angluin et al. [2004,2006] in order to model more powerful networks of resource-limited agents that are possibly mobile. The main feature of our extended model, called the Mediated Population Protocol (MPP) model, is to allow edges of the communication graph to have states that belong to a constant size set. We then allow the protocol rules for pairwise interactions to modify the corresponding edge state. Protocol specifications preserve both uniformity and anonymity. We first focus on the computational power of the MPP model on complete communication graphs and initially identical edges. We provide the following exact characterization for the class MPS of stably computable predicates: A predicate is in MPS iff it is symmetric and is in NSPACE(n^2)$. We finally ignore the input to the agents and study MPP's ability to compute graph properties.

Abstract: We extend here the Population Protocol model of Angluin et al. [2004] in order to model more powerful networks of very small resource-limited artefacts (agents) that are possibly mobile. Communication can happen only between pairs of artefacts. A communication graph (or digraph) denotes the permissible pairwise interactions. The main feature of our extended model is to allow edges of the communication graph, G, to have states that belong to a constant size set. We also allow edges to have readable only costs, whose values also belong to a constant size set. We then allow the protocol rules for pairwise interactions to modify the corresponding edge state. Thus, our protocol specifications are still independent of the population size and do not use agent ids, i.e. they preserve scalability, uniformity and anonymity. Our Mediated Population Protocols (MPP) can stably compute graph properties of the communication graph. We show this for the properties of maximal matchings (in undirected communication graphs), also for finding the transitive closure of directed graphs and for finding all edges of small cost. We demonstrate that our mediated protocols are stronger than the classical population protocols, by presenting a mediated protocol that stably computes the product of two positive integers, when G is the complete graph. This is not a semilinear predicate. To show this fact, we state and prove a general Theorem about the Composition of two stably computing mediated population protocols. We also show that all predicates stably computable in our model are (non-uniformly) in the class NSPACE(m), where m is the number of edges of the communication graph. We also define Randomized MPP and show that, any Peano predicate accepted by a MPP, can be verified in deterministic Polynomial Time.

Abstract: Evolutionary dynamics have been traditionally studied in the context of homogeneous populations, mainly described by the Moran process [15]. Recently, this approach has been generalized in [13] by arranging individuals on the nodes of a network (in general, directed). In this setting, the existence of directed arcs enables the simulation of extreme phenomena, where the fixation probability of a randomly placed mutant (i.e. the probability that the offsprings of the mutant eventually spread over the whole population) is arbitrarily small or large. On the other hand, undirected networks (i.e. undirected graphs) seem to have a smoother behavior, and thus it is more challenging to find suppressors/amplifiers of selection, that is, graphs with smaller/greater fixation probability than the complete graph (i.e. the homogeneous population). In this paper we focus on undirected graphs. We present the first class of undirected graphs which act as suppressors of selection, by achieving a fixation probability that is at most one half of that of the complete graph, as the number of vertices increases. Moreover, we provide some generic upper and lower bounds for the fixation
probability of general undirected graphs. As our main contribution, we introduce the natural alternative of the model proposed in [13]. In our new evolutionary model, all individuals interact simultaneously and the result is a compromise between aggressive and non-aggressive individuals. That is, the behavior of the individuals in our new model and in the model of [13] can be interpreted as an “aggregation” vs. an “all-or-nothing” strategy, respectively. We prove that our new model of mutual influences admits a potential function, which guarantees the convergence of the system for any graph topology and any initial fitness vector of the individuals. Furthermore, we prove fast convergence to the stable state for the case of the complete graph, as well as we provide almost tight bounds on the limit fitness of the individuals. Apart from being important on its own, this new evolutionary model appears to be useful also in the abstract modeling of control mechanisms over invading populations in networks. We demonstrate this by introducing and analyzing two alternative control approaches, for which we bound the time needed to stabilize to the “healthy” state of the system.

Abstract: We propose new burst assembly schemes and fast reservation (FR) protocols for Optical Burst Switched (OBS) networks that are based on traffic prediction. The burst assembly schemes aim at minimizing (for a given burst size) the average delay of the packets incurred during the burst assembly process, while the fast reservation protocols aim at further reducing the end-to-end delay of the data bursts. The burst assembly techniques use a linear prediction filter to estimate the number of packet arrivals at the ingress node in the following interval, and launch a new burst into the network when a certain criterion, different for each proposed scheme, is met. The fast reservation protocols use prediction filters to estimate the expected length of the burst and the time needed for the burst assembly process to complete. A Burst Header Packet (BHP) packet carrying these estimates is sent before the burst is completed, in order to reserve bandwidth at intermediate nodes for the time interval the burst is expected to pass from these nodes. Reducing the packet aggregation delay and the time required to perform the reservations, reduces the total time needed for a packet to be transported over an OBS network and is especially important for real-time applications. We evaluate the performance of the proposed burst assembly schemes and show that a number of them outperform the previously proposed timer-based, length-based and average delay-based burst assembly schemes. We also look at the performance of the fast reservation (FR) protocols in terms of the probability of successfully establishing the reservations required to transport the burst.

Abstract: Wireless Sensor Networks (WSNs) constitute a recent and promising new
technology that is widely applicable. Due to the applicability of this
technology and its obvious importance for the modern distributed
computational world, the formal scientific foundation of its inherent laws
becomes essential. As a result, many new computational models for WSNs
have been proposed. Population Protocols (PPs) are a special category of
such systems. These are mainly identified by three distinctive
characteristics: the sensor nodes (agents) move passively, that is, they
cannot control the underlying mobility pattern, the available memory to
each agent is restricted, and the agents interact in pairs. It has been
proven that a predicate is computable by the PP model iff it is
semilinear. The class of semilinear predicates is a fairly small class. In
this work, our basic goal is to enhance the PP model in order to improve
the computational power. We first make the assumption that not only the
nodes but also the edges of the communication graph can store restricted
states. In a complete graph of n nodes it is like having added O(n2)
additional memory cells which are only read and written by the endpoints
of the corresponding edge. We prove that the new model, called Mediated
Population Protocol model, can operate as a distributed nondeterministic
Turing machine (TM) that uses all the available memory. The only
difference from a usual TM is that this one computes only symmetric
languages. More formally, we establish that a predicate is computable by
the new model iff it is symmetric and belongs to NSPACE(n2). Moreover, we
study the ability of the new model to decide graph languages (for general
graphs). The next step is to ignore the states of the edges and provide
another enhancement straight away from the PP model. The assumption now is
that the agents are multitape TMs equipped with infinite memory, that can
perform internal computation and interact with other agents, and we define
space-bounded computations. We call this the Passively mobile Machines
model. We prove that if each agent uses at most f(n) memory for f(n)={\`U}(log
n) then a predicate is computable iff it is symmetric and belongs to
NSPACE(nf(n)). We also show that this is not the case for f(n)=o(log n).
Based on these, we show that for f(n)={\`U}(log n) there exists a space
hierarchy like the one for classical symmetric TMs. We also show that the
latter is not the case for f(n)=o(loglog n), since here the corresponding
class collapses in the class of semilinear predicates and finally that for
f(n)={\`U}(loglog n) the class becomes a proper superset of semilinear
predicates. We leave open the problem of characterizing the classes for
f(n)={\`U}(loglog n) and f(n)=o(log n).

Abstract: The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. The Radiocoloring (RC) of a graph G(V,E) is an assignment function Φ: V → IN such that ¦Φ(u)-Φ(v)≥ 2, when u; v are neighbors in G, and ¦Φ(u)-Φ(v)≥1 when the minimum distance of u; v in G is two. The discrete number and the range of frequencies used are called order and span, respectively. The optimization versions of the Radiocoloring Problem (RCP) are to minimize the span or the order. In this paper we prove that the min span RCP is NP-complete for planar graphs. Next, we provide an O(nΔ) time algorithm (¦V¦ = n) which obtains a radiocoloring of a planar graph G that approximates the minimum order within a ratio which tends to 2 (where Δ the maximum degree of G). Finally, we provide a fully polynomial randomized approximation scheme (fpras) for the number of valid radiocolorings of a planar graph G with λ colors, in the case λ ≥ 4λ + 50.

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: 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: We present a detailed performance evaluation of a
hybrid optical switching architecture called Overspill Routing in
Optical Networks (ORION). The ORION architecture combines
wavelength and (electronic) packet switching, so as to obtain the
advantages of both switching paradigms. We have developed an
extensive network simulator where the basic features of the
ORION architecture were modeled, including suitable loadvarying
sources and edge/core node architectures. Various aspects
of the ORION architecture were studied including the routing
policies used (i.e. once ORION always ORION and lightpath reentry)
and the various options available for the buffer
architecture. The completenetwork study shows that ORION can
absorb temporary traffic overloads, as intended, provided
sufficient buffering is present.

Abstract: In this work we extend the population protocol model of Angluin et al., in
order to model more powerful networks of very small resource limited
artefacts (agents) that is possible to follow some unpredictable passive
movement. These agents communicate in pairs according to the commands of
an adversary scheduler. A directed (or undirected) communication graph
encodes the following information: each edge (u,\~{o}) denotes that during the
computation it is possible for an interaction between u and \~{o} to happen in
which u is the initiator and \~{o} the responder. The new characteristic of
the proposed mediated population protocol model is the existance of a
passive communication provider that we call mediator. The mediator is a
simple database with communication capabilities. Its main purpose is to
maintain the permissible interactions in communication classes, whose
number is constant and independent of the population size. For this reason
we assume that each agent has a unique identifier for whose existence the
agent itself is not informed and thus cannot store it in its working
memory. When two agents are about to interact they send their ids to the
mediator. The mediator searches for that ordered pair in its database and
if it exists in some communication class it sends back to the agents the
state corresponding to that class. If this interaction is not permitted to
the agents, or, in other words, if this specific pair does not exist in
the database, the agents are informed to abord the interaction. Note that
in this manner for the first time we obtain some control on the safety of
the network and moreover the mediator provides us at any time with the
network topology. Equivalently, we can model the mediator by communication
links that are capable of keeping states from a edge state set of constant
cardinality. This alternative way of thinking of the new model has many
advantages concerning the formal modeling and the design of protocols,
since it enables us to abstract away the implementation details of the
mediator. Moreover, we extend further the new model by allowing the edges
to keep readable only costs, whose values also belong to a constant size
set. We then allow the protocol rules for pairwise interactions to modify
the corresponding edge state by also taking into account the costs. Thus,
our protocol descriptions are still independent of the population size and
do not use agent ids, i.e. they preserve scalability, uniformity and
anonymity. The proposed Mediated Population Protocols (MPP) can stably
compute graph properties of the communication graph. We show this for the
properties of maximal matchings (in undirected communication graphs), also
for finding the transitive closure of directed graphs and for finding all
edges of small cost. We demonstrate that our mediated protocols are
stronger than the classical population protocols. First of all we notice
an obvious fact: the classical model is a special case of the new model,
that is, the new model can compute at least the same things with the
classical one. We then present a mediated protocol that stably computes
the product of two nonnegative integers in the case where G is complete
directed and connected. Such kind of predicates are not semilinear and it
has been proven that classical population protocols in complete graphs can
compute precisely the semilinear predicates, thus in this manner we show
that there is at least one predicate that our model computes and which the
classical model cannot compute. To show this fact, we state and prove a
general Theorem about the composition of two mediated population
protocols, where the first one has stabilizing inputs. We also show that
all predicates stably computable in our model are (non-uniformly) in the
class NSPACE(m), where m is the number of edges of the communication
graph. Finally, we define Randomized MPP and show that, any Peano
predicate accepted by a Randomized MPP, can be verified in deterministic
polynomial time.

Abstract: This is a joint work with Ioannis Chatzigiannakis and Othon Michail.
We discuss here the population protocol model and most of its well-known extensions. The population protocol model aims to represent sensor networks consisting of tiny computational devices with sensing capabilities that follow some unpredictable and uncontrollable mobility pattern. It adopts a minimalistic approach and, thus, naturally computes a quite restricted class of predicates and exhibits almost no fault-tolerance. Most recent approaches make extra realistic and implementable assumptions, in order to gain more computational power and/or speed-up the time to convergence and/or improve fault-tolerance. In particular, the mediated population protocol model, the community protocol model, and the PALOMA model, which are all extensions of the population protocol model, are thoroughly discussed. Finally, the inherent difficulty of verifying the correctness of population protocols that run on complete communication graphs is revealed, but a promising algorithmic solution is presented.

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: The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters, by exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. A Radiocoloring (RC) of a graph G(V,E) is an assignment function View the MathML source such that |{\"O}(u)-{\"O}(v)|greater-or-equal, slanted2, when u,v are neighbors in G, and |{\"O}(u)-{\"O}(v)|greater-or-equal, slanted1 when the distance of u,v in G is two. The number of discrete frequencies and the range of frequencies used are called order and span, respectively. The optimization versions of the Radiocoloring Problem (RCP) are to minimize the span or the order. In this paper we prove that the radiocoloring problem for general graphs is hard to approximate (unless NP=ZPP) within a factor of n1/2-{\aa} (for any View the MathML source), where n is the number of vertices of the graph. However, when restricted to some special cases of graphs, the problem becomes easier. We prove that the min span RCP is NP-complete for planar graphs. Next, we provide an O(n{\"A}) time algorithm (|V|=n) which obtains a radiocoloring of a planar graph G that approximates the minimum order within a ratio which tends to 2 (where {\"A} the maximum degree of G). Finally, we provide a fully polynomial randomized approximation scheme (fpras) for the number of valid radiocolorings of a planar graph G with {\"e} colors, in the case where {\"e}greater-or-equal, slanted4{\"A}+50.

Abstract: The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters, by exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. A Radiocoloring (RC) of a graph G(V,E) is an assignment function View the MathML source such that |{\"O}(u)-{\"O}(v)|greater-or-equal, slanted2, when u,v are neighbors in G, and |{\"O}(u)-{\"O}(v)|greater-or-equal, slanted1 when the distance of u,v in G is two. The number of discrete frequencies and the range of frequencies used are called order and span, respectively. The optimization versions of the Radiocoloring Problem (RCP) are to minimize the span or the order. In this paper we prove that the radiocoloring problem for general graphs is hard to approximate (unless NP=ZPP) within a factor of n1/2-{\aa} (for any View the MathML source), where n is the number of vertices of the graph. However, when restricted to some special cases of graphs, the problem becomes easier. We prove that the min span RCP is NP-complete for planar graphs. Next, we provide an O(n{\"A}) time algorithm (|V|=n) which obtains a radiocoloring of a planar graph G that approximates the minimum order within a ratio which tends to 2 (where {\"A} the maximum degree of G). Finally, we provide a fully polynomial randomized approximation scheme (fpras) for the number of valid radiocolorings of a planar graph G with {\"e} colors, in the case where {\"e}greater-or-equal, slanted4{\"A}+50.

Abstract: The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. A Radiocoloring (RC) of a graph G(V,E) is an assignment function View the MathML source such that |{\"E}(u)−{\"E}(v)|greater-or-equal, slanted2, when u,v are neighbors in G, and |{\"E}(u)−{\"E}(v)|greater-or-equal, slanted1 when the distance of u,v in G is two. The discrete number of frequencies used is called order and the range of frequencies used, span. The optimization versions of the Radiocoloring Problem (RCP) are to minimize the span (min span RCP) or the order (min order RCP).
In this paper, we deal with an interesting, yet not examined until now, variation of the radiocoloring problem: that of satisfying frequency assignment requests which exhibit some periodic behavior. In this case, the interference graph (modelling interference between transmitters) is some (infinite) periodic graph. Infinite periodic graphs usually model finite networks that accept periodic (in time, e.g. daily) requests for frequency assignment. Alternatively, they can model very large networks produced by the repetition of a small graph.
A periodic graph G is defined by an infinite two-way sequence of repetitions of the same finite graph Gi(Vi,Ei). The edge set of G is derived by connecting the vertices of each iteration Gi to some of the vertices of the next iteration Gi+1, the same for all Gi. We focus on planar periodic graphs, because in many cases real networks are planar and also because of their independent mathematical interest.
We give two basic results:
• We prove that the min span RCP is PSPACE-complete for periodic planar graphs.
• We provide an O(n({\"A}(Gi)+{\'o})) time algorithm (where|Vi|=n, {\"A}(Gi) is the maximum degree of the graph Gi and {\'o} is the number of edges connecting each Gi to Gi+1), which obtains a radiocoloring of a periodic planar graph G that approximates the minimum span within a ratio which tends to View the MathML source as {\"A}(Gi)+{\'o} tends to infinity.
We remark that, any approximation algorithm for the min span RCP of a finite planar graph G, that achieves a span of at most {\'a}{\"A}(G)+constant, for any {\'a} and where {\"A}(G) is the maximum degree of G, can be used as a subroutine in our algorithm to produce an approximation for min span RCP of asymptotic ratio {\'a} for periodic planar graphs.

Abstract: The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. The Radiocoloring (RC) of a graph G(V,E) is an assignment function {\"O}: V → IN such that ∣{\"O}(u) - {\"O}(v)∣ ≥2, when u, v are neighbors in G, and ∣{\"O}(u) - {\"O}(v)∣ ≥1 when the distance of u, v in G is two. The range of frequencies used is called span. Here, we consider the optimization version of the Radiocoloring Problem (RCP) of finding a radiocoloring assignment of minimum span, called min span RCP. In this paper, we deal with a variation of RCP: that of satisfying frequency assignment requests with some periodic behavior. In this case, the interference graph is an (infinite) periodic graph. Infinite periodic graphs model finite networks that accept periodic (in time, e.g. daily) requests for frequency assignment. Alternatively, they may model very large networks produced by the repetition of a small graph. A periodic graph G is defined by an infinite two-way sequence of repetitions of the same finite graph G i (V i ,E i ). The edge set of G is derived by connecting the vertices of each iteration G i to some of the vertices of the next iteration G i +1, the same for all G i . The model of periodic graphs considered here is similar to that of periodic graphs in Orlin [13], Marathe et al [10]. We focus on planar periodic graphs, because in many cases real networks are planar and also because of their independent mathematical interest. We give two basic results: - We prove that the min span RCP is PSPACE-complete for periodic planar graphs. - We provide an O(n({\"A}(G i ) + {\'o})) time algorithm, (where ∣V i ∣ = n, {\"A}(G i ) is the maximum degree of the graph G i and {\'o} is the number of edges connecting each G i to G i +1), which obtains a radiocoloring of a periodic planar graph G that approximates the minimum span within a ratio which tends to 2 as {\"A}(Gi) + {\'o} tends to infinity.

Abstract: We propose information aggregation as a method for summarizing the resource-related information, used by the task scheduler. Through this method the information of a set of resources can be uniformly represented, reducing at the same time the amount of information transferred in a Grid network. A number of techniques are described for aggregating the information of the resources belonging to a hierarchical Grid domain. This information includes the cpu and storage capacities at a site, the number of tasks queued, and other resource-related parameters. The quality of the aggregation scheme affects the efficiency of the scheduler{\^a}€™s decisions. We use as a metric of aggregation efficiency the Stretch Factor (SF), defined as the ratio of the task delay when the task is scheduled using complete resource information over the task delay when an aggregation scheme is used. The simulation experiments performed show that the proposed aggregation schemes achieve large information reduction, while enabling good task scheduling decisions as indicated by the SF achieved.

Abstract: We explore the capability of a network of extremely limited
computational entities to decide properties about any of its subnetworks.
We consider that the underlying network of the interacting
entities (devices, agents, processes etc.) is modeled by a complete in-
teraction graph and we devise simple graph protocols that can decide
properties of some input subgraph provided by some preprocessing on
the network. The agents are modeled as nite-state automata and run
the same global graph protocol. Each protocol is a xed size grammar,
that is, its description is independent of the size (number of agents) of
the network. This size is not known by the agents. We propose a simple
model, the Mediated Graph Protocol (MGP) model, similar to the Population
Protocol model of Angluin et al., in which each network link is
characterized by a state taken from a nite set. This state can be used
and updated during each interaction between the corresponding agents.
We provide some interesting properties of the MGP model among which
is the ability to decide properties on stabilizing (initially changing for a
nite number of steps) input graphs and we show that the MGP model
has the ability to decide properties of disconnected input graphs. We
show that the computational power within the connected components is
fairly restricted. Finally, we give an exact characterization of the class
GMGP, of graph languages decidable by the MGP model: it is equal
to the class of graph languages decidable by a nondeterministic Turing
Machine of linear space that receives its input graph by its adjacency
matrix representation.

Abstract: We explore the capability of a network of extremely limited computational entities to decide properties about itself or any of its subnetworks. We consider that the underlying network of the interacting entities (devices, agents, processes etc.) is modeled by an interaction graph that reflects the network’s connectivity. We examine the following two cases: First, we consider the case where the input graph is the whole interaction graph and second where it is some subgraph of the interaction graph given by some preprocessing on the network. In each case, we devise simple graph protocols that can decide properties of the input graph. The computational entities, that are called agents, are modeled as finite-state automata and run the same global graph protocol. Each protocol is a fixed size grammar, that is, its description is independent of the size (number of agents) of the network. This size is not known by the agents. We present two simple models (one for each case), the Graph Decision Mediated Population Protocol (GDMPP) and the Mediated Graph Protocol (MGP) models, similar to the Population Protocol model of Angluin et al., where each network link (edge of the interaction graph) is characterized by a state taken from a finite set. This state can be used and updated during each interaction between the corresponding agents. We provide some example protocols and some interesting properties for the two models concerning the computability of graph languages in various settings (disconnected input graphs, stabilizing input graphs). We show that the computational power within the family of all (at least) weakly-connected input graphs is fairly restricted. Finally, we give an exact characterization of the class of graph languages decidable by the MGP model in the case of complete interaction graphs: it is equal to the class of graph languages decidable by a nondeterministic Turing Machine of linear space that receives its input graph by its adjacency matrix representation.

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: The peer-to-peer computing paradigm is an intriguing alternative to Google-style search
engines for querying and ranking Web content. In a network with many thousands or
millions of peers the storage and access load requirements per peer are much lighter
than for a centralized Google-like server farm; thus more powerful techniques from information
retrieval, statistical learning, computational linguistics, and ontological reasoning
can be employed on each peer¢s local search engine for boosting the quality
of search results. In addition, peers can dynamically collaborate on advanced and particularly
difficult queries. Moroever, a peer-to-peer setting is ideally suited to capture
local user behavior, like query logs and click streams, and disseminate and aggregate
this information in the network, at the discretion of the corresponding user, in order to
incorporate richer cognitive models.
This paper gives an overview of ongoing work in the EU Integrated Project DELIS
that aims to develop foundations for a peer-to-peer search engine with Google-or-better
scale, functionality, and quality, which will operate in a completely decentralized and
self-organizing manner. The paper presents the architecture of such a system and the
Minerva prototype testbed, and it discusses various core pieces of the approach: efficient
execution of top-k ranking queries, strategies for query routing when a search request
needs to be forwarded to other peers, maintaining a self-organizing semantic overlay
network, and exploiting and coping with user and community behavior.

Abstract: We examine the problem of transmitting in minimum time a given amount of data between a
source and a destination in a network with finite channel capacities and nonzero propagation delays. In
the absence of delays, the problem has been shown to be solvable in polynomial time. In this paper, we
show that the general problem is NP-complete. In addition, we examine transmissions along a single path,
called the quickest path, and present algorithms for general and special classes of networks that improve
upon previous approaches. The first dynamic algorithm for the quickest path problem is also
given