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- W1978447499 abstract "Given an undirected graph $G$, a collection ${(s_1,t_1), dots, (s_{k},t_{k})}$ of pairs of vertices, and an integer ${{p}}$, the Edge Multicut problem asks if there is a set $S$ of at most ${{p}}$ edges such that the removal of $S$ disconnects every $s_i$ from the corresponding $t_i$. Vertex Multicut is the analogous problem where $S$ is a set of at most ${{p}}$ vertices. Our main result is that both problems can be solved in time $2^{O({{p}}^3)}cdot n^{O(1)}$, i.e., fixed-parameter tractable parameterized by the size ${{p}}$ of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form $f({{p}})cdot n^{O(1)}$ exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset." @default.
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- W1978447499 date "2014-01-01" @default.
- W1978447499 modified "2023-10-01" @default.
- W1978447499 title "Fixed-Parameter Tractability of Multicut Parameterized by the Size of the Cutset" @default.
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- W1978447499 doi "https://doi.org/10.1137/110855247" @default.
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