Faster exact algorithms for some terminal set problems

Many problems on graphs can be expressed in the following language: given a graph G=(V,E) and a terminal set T⊆V, find a minimum size set S⊆V which intersects all “structures” (such as cycles or paths) passing through the vertices in T. We refer to this class of problems as terminal set problems. In...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 88; pp. 195 - 207
Main Authors: Chitnis, Rajesh, Fomin, Fedor V., Lokshtanov, Daniel, Misra, Pranabendu, Ramanujan, M.S., Saurabh, Saket
Format: Journal Article
Language:English
Published: Elsevier Inc 01.09.2017
Subjects:
Exact exponential time algorithms
Feedback vertex set
Multiway cut
Terminal set problems
Exact exponential time algorithms
Multiway cut
Terminal set problems
Feedback vertex set
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary:Many problems on graphs can be expressed in the following language: given a graph G=(V,E) and a terminal set T⊆V, find a minimum size set S⊆V which intersects all “structures” (such as cycles or paths) passing through the vertices in T. We refer to this class of problems as terminal set problems. In this paper, we introduce a general method to obtain faster exact exponential time algorithms for several terminal set problems. In the process, we break the O⁎(2n) barrier for the classic Node Multiway Cut, Directed Unrestricted Node Multiway Cut and Directed Subset Feedback Vertex Set problems. •A general methodology to obtain faster exact exponential time algorithms well-studied terminal set problems is presented.•It combines polynomial time, fixed parameter tractable and exact exponential time algorithms for the non-terminal versions.•We break the O⁎(2n) barrier for the classic Node Multiway Cut and Directed Subset Feedback Vertex Set problems.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2017.04.003