Abstract
We study a Network Security question that consists of learning where are the most important checkpoints to intercept an adversary traveling from an origin to a destination. For that we define a cooperative game where every player controls an arc, and is able to place a checkpoint on it. We assume that the adversary is trying to travel from s to t. If the adversary crosses a checkpoint there is no certainty that he will be detected, therefore the value of a coalition should reflect the number of checkpoints, in the coalition, that the adversary has to cross (the more, the better). This suggests defining the value of a coalition S as the maximum number of disjoint st-cuts included in S; this is a lower bound for the number of checkpoints in S that the adversary has to cross. The adversary can choose any shortest path (minimum cardinality) from s to t, so in any particular coalition one cannot know the exact number of checkpoints that he will cross, and thus we propose to work with a lower bound instead. We give a polynomial combinatorial algorithm for computing the nucleolus of this game. The nucleolus is an allocation of resources to each arc that reflects the contribution of each checkpoint to the common objective of detecting the adversary. The larger values in the nucleolus indicate the more important locations.
Highlights
We study a Network Security issue, namely deciding where are the most important locations to place checkpoints, in a transportation or a communication network, to detect an adversary trying to travel from a node s to a node t
If the adversary crosses a checkpoint there is no certainty that he will be detected, and the value of a coalition should reflect the number of checkpoints, in the coalition, that the adversary has to cross. This suggests to define the value of a coalition S as the maximum number of disjoint st-cuts included in S; this is a lower bound for the number of checkpoints in the coalition that the adversary has to cross
For an arc-set S we need to compute the maximum number of disjoint st-cuts included in S, here we show that a primaldual version of Dijkstra’s algorithm [11], for shortest paths, can be used
Summary
We study a Network Security issue, namely deciding where are the most important locations to place checkpoints, in a transportation or a communication network, to detect an adversary trying to travel from a node s to a node t. Related work on this type of games is the following This game is dual to a flow game studied in [18], where the value of a coalition S ⊆ A is the maximum number of disjoint st-paths included in S. The core of this flow game has been studied in [18], and the nucleolus has been studied in [9] and [22]. A polynomial algorithm to compute the -core was given in [3] This (zero-one) value function is useful under the assumption that the adversary is detected each time that he crosses a checkpoint, on the other hand, our (different) value function let us deal with the uncertainty of detection.
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