Fixed-Parameter Tractability of Multicut Parameterized by the Size of the Cutset
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 Mult...
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| Vydáno v: | SIAM journal on computing Ročník 43; číslo 2; s. 355 - 388 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2014
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| Témata: | |
| ISSN: | 0097-5397, 1095-7111 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. [PUBLICATION ABSTRACT] |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0097-5397 1095-7111 |
| DOI: | 10.1137/110855247 |