Finding a Nonempty Algebraic Subset of an Edge Set in Linear Time
Vol. 11, no. 1, pp. 239-257, 2007. Regular paper.
Abstract A set of edges of a hypergraph H is an algebraic set if its characteristic vector can be expressed as a linear combination of rows of the (node-edge) incidence matrix of H. Recently it was proven that deciding whether or not a given edge-set of H contains a non-empty algebraic set is an NP-complete problem. In this paper we give a linear time algorithm to decide if a given edge-set contains a non-empty algebraic set when the hypergraph is a graph.
Submitted: November 2005.
Revised: January 2007.
Communicated by Larse Arge
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