Finding small separators in linear time via treewidth reduction

Marx, D. and O'Sullivan, B. and Razgon, Igor (2013) Finding small separators in linear time via treewidth reduction. ACM Transactions on Algorithms 9 (4), p. 30. ISSN 1549-6325.

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Official URL: http://dx.doi.org/10.1145/2500119

Abstract

We present a method for reducing the treewidth of a graph while preserving all of its minimal $s-t$ separators up to a certain fixed size $k$. This technique allows us to solve $s-t$ Cut and Multicut problems with various additional restrictions (e.g., the vertices being removed from the graph form an independent set or induce a connected graph) in linear time for every fixed number $k$ of removed vertices. Our results have applications for problems that are not directly defined by separators, but the known solution methods depend on some variant of separation. for example, we can solve similarly restricted generalizations of Bipartization (delete at most $k$ vertices from $G$ to make it bipartite) in almost linear time for every fixed number $k$ of removed vertices. These results answer a number of open questions in the area of parameterized complexity. Furthermore, our technique turns out to be relevant for $(H,C,K)$- and $(H,C,\le K)$-coloring problems as well, which are cardinality constrained variants of the classical $H$-coloring problem. We make progress in the classification of the parameterized complexity of these problems by identifying new cases that can be solved in almost linear time for every fixed cardinality bound.

Metadata

Item Type:	Article
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Administrator
Date Deposited:	08 Oct 2013 14:15
Last Modified:	09 Aug 2023 12:33
URI:	https://eprints.bbk.ac.uk/id/eprint/7586

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