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In a distributed system with attacks and defenses, both attackers and defenders are selfinterested entities. We assume a reward-sharing scheme among interdependent defenders; each defender wishes to (locally) maximize her own total fair... more
In a distributed system with attacks and defenses, both attackers and defenders are selfinterested
entities. We assume a reward-sharing scheme among interdependent defenders;
each defender wishes to (locally) maximize her own total fair share to the attackers extinguished
due to her involvement (and possibly due to those of others). What is the maximum
amount of protection achievable by a number of such defenders against a number of attackers
while the system is in a Nash equilibrium? As a measure of system protection, we adopt
the Defense-Ratio (Mavronicolas et al., 2008) [20], which provides the expected (inverse)
proportion of attackers caught by the defenders. In a Defense-Optimal Nash equilibrium,
the Defense-Ratio matches a simple lower bound.
We discover that the existence of Defense-Optimal Nash equilibria depends in a subtle
way on how the number of defenders compares to two natural graph-theoretic thresholds
we identify. In this vein, we obtain, through a combinatorial analysis of Nash equilibria, a
collection of trade-off results:
• When the number of defenders is either sufficiently small or sufficiently large, Defense-
Optimal Nash equilibria may exist. The corresponding decision problem is computationally
tractable for a large number of defenders; the problem becomesNP-complete
for a small number of defenders and the intractability is inherited from a previously unconsidered
combinatorial problem in Fractional Graph Theory.
• Perhaps paradoxically, there is a middle range of values for the number of defenders
where Defense-Optimal Nash equilibria do not exist.
entities. We assume a reward-sharing scheme among interdependent defenders;
each defender wishes to (locally) maximize her own total fair share to the attackers extinguished
due to her involvement (and possibly due to those of others). What is the maximum
amount of protection achievable by a number of such defenders against a number of attackers
while the system is in a Nash equilibrium? As a measure of system protection, we adopt
the Defense-Ratio (Mavronicolas et al., 2008) [20], which provides the expected (inverse)
proportion of attackers caught by the defenders. In a Defense-Optimal Nash equilibrium,
the Defense-Ratio matches a simple lower bound.
We discover that the existence of Defense-Optimal Nash equilibria depends in a subtle
way on how the number of defenders compares to two natural graph-theoretic thresholds
we identify. In this vein, we obtain, through a combinatorial analysis of Nash equilibria, a
collection of trade-off results:
• When the number of defenders is either sufficiently small or sufficiently large, Defense-
Optimal Nash equilibria may exist. The corresponding decision problem is computationally
tractable for a large number of defenders; the problem becomesNP-complete
for a small number of defenders and the intractability is inherited from a previously unconsidered
combinatorial problem in Fractional Graph Theory.
• Perhaps paradoxically, there is a middle range of values for the number of defenders
where Defense-Optimal Nash equilibria do not exist.
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Research Interests: Algebraic Number Theory, Algebra, Computer Science, Grid Computing, Finite Element Methods, and 12 moreGraph Theory, Computational Modeling, Resource Allocation, Finite element method, Shape Optimization, Finite Element Analysis, Load Balancing, Shape, Acceleration, Graph Partitioning, Heuristic, and Load Balance
Research Interests: Computer Science, Parallel Algorithms, Distributed Computing, Mobile Ad Hoc Networks, Computer Networks, and 14 moreResource Allocation, Convergence, Mobile Computing, Mobile Ad Hoc Network, Ad Hoc Networks, Load Balancing, Convergence Rate, Ad hoc network, Network Topology, Load Balance, Eigenvalue Problems, Dynamic Networks, Intelligent Networks, and Load Balancing Algorithms
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In this paper, we present PQSOLVE, a distributed theorem-prover for Quantified Boolean Formulae. First, we introduce our sequential algorithm Q SOLVE, which uses new heuristics and improves the use of known heuristics to prune the search... more
In this paper, we present PQSOLVE, a distributed theorem-prover for Quantified Boolean Formulae. First, we introduce our sequential algorithm Q SOLVE, which uses new heuristics and improves the use of known heuristics to prune the search tree. As a result, Q SOLVE is more efficient than the QSAT-solvers previously known. We have parallelized QSOLVE. The resulting distributed QSAT-solver PQSOLVE uses parallel search techniques, which we have developed for distributed game tree search. PQSOLVE runs efficiently on dis- tributed systems, i. e. parallel systems without any shared memory. We briefly present experiments that show a speedup of about 114 on 128 processors. To the best of our knowledge we are the first to introduce an efficient parallel QSAT-solver.
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Research Interests: Computer Science, Distributed Computing, Graph Theory, Finite element method, Parallel Processing, and 13 moreAlgorithm, Optimization, Shape Optimization, Multigrid, Parallel & Distributed Computing, Load Balancing, Bubble, Graph Partitioning, Parallel Algorithm, Load Balance, Parallel and Distributed Processing, User Requirements, and Objective function
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Abstract. We study the problem of n users selfishly routing traffics through a shared network. Users route their traffics by choosing a path from their source to their destination of the traffic with the aim of min-imizing their private... more
Abstract. We study the problem of n users selfishly routing traffics through a shared network. Users route their traffics by choosing a path from their source to their destination of the traffic with the aim of min-imizing their private latency. In such an environment Nash equilibria ...
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Research Interests: Social Psychology, Computer Science, Game Theory, Image Processing, Computational Complexity, and 15 morePattern Recognition, Routing, Speech Processing, Hardness, Nash Equilibrium, Mathematical Optimization, Route, Randomized Algorithm, Random Polynomials, Latency, Channel Capacity, Nash equilibria, Objective function, Probability Distribution, and Polynomial Time
Research Interests: Sociology, Mathematics, Computer Science, Modeling, Communication Network, and 13 moreİnternet Network, Mathematical Optimization, Network Routing, Scenario, Telecommunication network, Community Networks, Economic Model, Network Topology, Price of Anarchy, Latency, Non-Cooperative Game Theory, Bottleneck, and Internet
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Research Interests: Mathematics, Computer Science, Approximation Algorithms, Scheduling, Time Use, and 12 moreTheoretical Computer Science, Algorithm, Mathematical Sciences, Interior Point Methods, APPROXIMATION ALGORITHM, Integrated Approach, Job shop scheduling, Bipartite Graph, Parallel Machines, Approximate Algorithm, Network Flow, and Pipage Rounding
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In the model of restricted parallel links, n users must be routed on m parallel links under the restriction that the link for each user be chosen from a certain set of allowed links for the user. In a (pure) Nash equilibrium, no user may... more
In the model of restricted parallel links, n users must be routed on m parallel links under the restriction that the link for each user be chosen from a certain set of allowed links for the user. In a (pure) Nash equilibrium, no user may improve its own Individual Cost (latency) by unilaterally switching to another link from its set of allowed links. The Price of Anarchy is a widely adopted measure of the worst-case loss (relative to optimum) in system performance (maximum latency) incurred in a Nash equilibrium. In this work, we present a comprehensive collection of bounds on Price of Anarchy for the model of restricted parallel links and for the special case of pure Nash equilibria. Specifically, we prove: • For the case of identical users and identical links, the Price of Anarchy is [Formula: see text]. • For the case of identical users, the Price of Anarchy is [Formula: see text]. • For the case of identical links, the Price of Anarchy is [Formula: see text], which is asymptotic...
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In this work we study weighted network congestion games with player-specific latency functions where selfish players wish to route their traffic through a shared network. We consider both the case of splittable and unsplittable traffic.... more
In this work we study weighted network congestion games with player-specific latency functions where selfish players wish to route their traffic through a shared network. We consider both the case of splittable and unsplittable traffic. Our main findings are as follows. For routing games on parallel links with linear latency functions, we introduce two new potential functions for unsplittable and for splittable traffic, respectively. We use these functions to derive results on the convergence to pure Nash equilibria and the computation of equilibria. For several generalizations of these routing games, we show that such potential functions do not exist. We prove tight upper and lower bounds on the price of anarchy for games with polynomial latency functions. All our results on the price of anarchy translate to general congestion games.