Skip to main content
Article thumbnail
Location of Repository

Transversals of subtree hypergraphs and the source location problem in digraphs

By Jan van den Heuvel and Matthew Johnson

Abstract

A hypergraph H = (V,E) is a subtree hypergraph if there is a tree T on V such that each hyperedge of E induces a subtree of T. To find a minimum size transversal for a subtree hypergraph is, in general, NP-hard. In this paper, we show that if it is possible to decide if a set of vertices W µ V is a transversal in time S(n) ( where n = |V | ), then it is possible to find a minimum size transversal in O(n3 S(n)). This result provides a polynomial algorithm for the Source Location Problem : a set of (k, l)-sources for a digraph D = (V,A) is a subset K of V such that for any v 2 V \ K there are k arc-disjoint paths that each join a vertex of K to v and l arc-disjoint paths that each join v to K. The Source Location Problem is to find a minimum size set of (k, l)-sources. We show that this is a case of finding a transversal of a subtree hypergraph, and that in this case S(n) is polynomial

Topics: QA Mathematics
Publisher: Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science
Year: 2004
OAI identifier: oai:eprints.lse.ac.uk:13347
Provided by: LSE Research Online
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://www.cdam.lse.ac.uk (external link)
  • http://eprints.lse.ac.uk/13347... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.