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Directed Multicut with linearly ordered terminals

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arxiv 1407.7498 v1 pith:GXBBK22J submitted 2014-07-28 cs.DS cs.CR

classification cs.DScs.CR
keywords directedsizealgorithmapplicationcasecutsetdistinguishededge
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abstract

Motivated by an application in network security, we investigate the following "linear" case of Directed Mutlicut. Let $G$ be a directed graph which includes some distinguished vertices $t_1, \ldots, t_k$. What is the size of the smallest edge cut which eliminates all paths from $t_i$ to $t_j$ for all $i < j$? We show that this problem is fixed-parameter tractable when parametrized in the cutset size $p$ via an algorithm running in $O(4^p p n^4)$ time.

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