Faster Algorithms for Security Games on Matroids

Baı̈ou, Mourad; Barahona, Francisco

doi:10.1007/s00453-018-0466-x

Cited by 4 publications

(6 citation statements)

References 19 publications

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“…holds for each edge e. Now assume that the Defender uses the following mixed strategy: for every 1 ≤ i ≤ t she assigns the probability α i to P i and 0 to the rest of the st-paths. Then if the Attacker targets an edge e then her expected loss is α i − c(e) ≤ d(e) (µp(e) + q(e)) − c(e) = µ by (2). Therefore this mixed strategy guarantees the Defender an expected loss of at most µ.…”

Section: Preliminaries On Game Theorymentioning

confidence: 91%

“…Furthermore, in the special case of c(e) ≡ 0 the result of [16,Corollary 51.8a] is essentially equivalent to the above theorem in a non-game-theoretical setting. The running time of the algorithm given in [17] was later substantially improved to O(|V | 4 |E| 1 2 ) in [2]. It also follows from the above theorem that the spanning tree game is capable of capturing a known graph reliability metric.…”

Section: Theoremmentioning

confidence: 99%

“…The existence of a strongly polynomial algorithm to compute the game value of the Arborescence Game and an optimum mixed strategy for both players was proved in [2].…”

Section: Theorem 2 ([17])mentioning

confidence: 99%

“…The following notion was defined and its computability in strongly polynomial time was proved in [17]. The running time was then again improved in [2].…”

Section: Theorem 2 ([17])mentioning

confidence: 99%

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Hitting a path: a generalization of weighted connectivity via game theory

Szeszlér

2018

J Comb Optim

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Applying game-theoretical tools for measuring the reliability of a network has become very common. The basic idea is very natural: analyzing an appropriately defined attacker-defender game might give rise to a relevant security metric. In this paper we consider a very natural set of games: the Defender chooses a path P between two given nodes and the Attacker chooses a network element a (that is, an edge or a node). In all cases, the Attacker has to pay a given cost of attack c(a); if, however, a is on P then he also gains a given profit of d(a). We determine the value of various versions of this game and show that the thus arising reliability metrics provide a generalization of weighted connectivity of graphs. We also prove that the values of the games and optimum mixed strategies for both players can be computed in strongly polynomial time.

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Section: Preliminaries On Game Theorymentioning

confidence: 91%

Section: Theoremmentioning

confidence: 99%

“…The existence of a strongly polynomial algorithm to compute the game value of the Arborescence Game and an optimum mixed strategy for both players was proved in [2].…”

Section: Theorem 2 ([17])mentioning

confidence: 99%

“…The following notion was defined and its computability in strongly polynomial time was proved in [17]. The running time was then again improved in [2].…”

Section: Theorem 2 ([17])mentioning

confidence: 99%

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Hitting a path: a generalization of weighted connectivity via game theory

Szeszlér

2018

J Comb Optim

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“…Since this game is a two-player, zero-sum game, it has a unique Nash-equilibrium payoff (or, in simpler terms, game value) V by Neumann's classic Minimax Theorem. Since V is the highest expected gain the Attacker can guarantee himself by an appropriately chosen mixed strategy (that is, probability distribution on the set of edges), it makes sense to say that 1 V is a valid reliability metric. After some preliminary results on some special cases in the literature (see [14] for the details), the Spanning Tree Game was solved in the above defined general form in [13].…”

Section: An Application: Reliability Of Network Via Game Theorymentioning

confidence: 99%

New polyhedral and algorithmic results on greedoids

Szeszlér

2019

Math. Program.

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We present various new results on greedoids. We prove a theorem that generalizes an equivalent formulation of Edmonds' classic matroid polytope theorem to local forest greedoids -a class of greedoids that contains matroids as well as branching greedoids. We also describe an application of this theorem in the field of measuring the reliability of networks by gametheoretical tools. Finally, we prove new results on the optimality of the greedy algorithm on greedoids and correct some mistakes that have been present in the literature for almost three decades.

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