Decomposition of Probability Marginals for Security Games in Max-Flow/Min-Cut Systems
Jannik Matuschke

TL;DR
This paper characterizes when a probability distribution satisfying certain marginals and security constraints exists in max-flow/min-cut systems, providing an efficient algorithm for a special case and connecting to security game equilibria.
Contribution
It establishes a necessary and sufficient condition for the existence of such distributions based on the weak max-flow/min-cut property and offers an efficient combinatorial algorithm for abstract networks.
Findings
Condition for distribution existence is both necessary and sufficient.
Efficient algorithm for abstract network cases.
Connection to security game equilibria and shortest path algorithms.
Abstract
Given a set system with and , our goal is to find a probability distribution for a random set such that for all and for all . We extend the results of Dahan, Amin, and Jaillet (MOR 2022) who studied this problem motivated by a security game in a directed acyclic graph (DAG). We focus on the setting where is of the affine form for . A necessary condition for the existence of the desired distribution is that for all . We show that this condition is sufficient if and only if has the weak max-flow/min-cut property. We further provide an efficient combinatorial…
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Complex Network Analysis Techniques
