Fixedparameter tractability of multicut parameterized by the size of the cutset
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 Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems 
Depositing User:  Administrator 
Date Deposited:  03 Jun 2016 09:37 
Last Modified:  03 Jun 2016 09:37 
URI:  http://eprints.bbk.ac.uk/id/eprint/15407 
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