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

1 Citaat (Scopus)

## 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-2 Engels Graph-Theoretic Concepts in Computer Science : 41st International Workshop, WG 2015, Garching, Germany, June 17-19, 2015 E.W. Mayr Berlin Springer 472-486 978-3-662-53174-7 978-3-662-53173-0 https://doi.org/10.1007/978-3-662-53174-7_33 Gepubliceerd - 5 aug 2016 41st International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2015), June 17-19, 2015, Munich, Germany - Munich, DuitslandDuur: 17 jun 2015 → 19 jun 2015http://wwwmayr.in.tum.de/konferenzen/WG2015/

### Publicatie series

Naam Lecture Notes in Computer Science 9224 0302-9743

### Workshop

Workshop 41st International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2015), June 17-19, 2015, Munich, Germany WG 2015 Duitsland Munich 17/06/15 → 19/06/15 41st International Workshop on Graph-Theoretic Concepts in Computer Science http://wwwmayr.in.tum.de/konferenzen/WG2015/