On structural parameterizations of hitting set: hitting paths in graphs using 2-SAT

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Samenvatting

Hitting Set is a classic problem in combinatorial optimization. Its input consists of a set system F over a finite universe U and an integer t; the question is whether there is a set of t elements that intersects every set in F. The Hitting Set problem parameterized by the size of the solution is a well-known W[2]-complete problem in parameterized complexity theory. In this paper we investigate the complexity of Hitting Set under various structural parameterizations of the input. Our starting point is the folklore result that Hitting Set is polynomial-time solvable if there is a tree T on vertex set U such that the sets in F induce connected subtrees of T. We consider the case that there is a treelike graph with vertex set U such that the sets in F induce connected subgraphs; the parameter of the problem is a measure of how treelike the graph is. Our main positive result is an algorithm that, given a graph G with cyclomatic number k, a collection P of simple paths in G, and an integer t, determines in time 2^{5k} (|G| +|P|)^O(1) whether there is a vertex set of size t that hits all paths in P. It is based on a connection to the 2-SAT problem in multiple valued logic. For other parameterizations we derive W[1]-hardness and para-NP-completeness results.
Originele taal-2Engels
TitelGraph-Theoretic Concepts in Computer Science : 41st International Workshop, WG 2015, Garching, Germany, June 17-19, 2015
RedacteurenE.W. Mayr
Plaats van productieBerlin
UitgeverijSpringer
Pagina's472-486
ISBN van elektronische versie978-3-662-53174-7
ISBN van geprinte versie978-3-662-53173-0
DOI's
StatusGepubliceerd - 5 aug 2016
Evenement41st International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2015), June 17-19, 2015, Munich, Germany - Munich, Duitsland
Duur: 17 jun 201519 jun 2015
http://wwwmayr.in.tum.de/konferenzen/WG2015/

Publicatie series

NaamLecture Notes in Computer Science
Volume9224
ISSN van geprinte versie0302-9743

Workshop

Workshop41st International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2015), June 17-19, 2015, Munich, Germany
Verkorte titelWG 2015
LandDuitsland
StadMunich
Periode17/06/1519/06/15
Ander41st International Workshop on Graph-Theoretic Concepts in Computer Science
Internet adres

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