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.Full text not available from this repository.
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)|
|Additional Information:||© 2004 the authors|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
|Date Deposited:||20 Nov 2008 10:42|
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