Marx, D. and Razgon, Igor (2014) Fixedparameter tractability of multicut parameterized by the size of the cutset. SIAM Journal on Computing 43 (2), pp. 355388. ISSN 00975397.

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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., fixedparameter 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.
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Item Type:  Article 

School:  Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences 
Depositing User:  Administrator 
Date Deposited:  03 Jun 2016 09:37 
Last Modified:  09 Aug 2023 12:38 
URI:  https://eprints.bbk.ac.uk/id/eprint/15407 
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