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Transversals of subtree hypergraphs and the source location problem in digraphs

van den Heuvel, Jan and Johnson, Matthew (2004) Transversals of subtree hypergraphs and the source location problem in digraphs. CDAM research report series, CDAM-2004-10. Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.

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Identification Number: CDAM-2004-10

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.

Item Type: Monograph (Report)
Official URL: http://www.cdam.lse.ac.uk
Additional Information: © 2004 the authors
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 20 Nov 2008 10:42
Last Modified: 01 Oct 2010 09:05
URI: http://eprints.lse.ac.uk/id/eprint/13347

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