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Mixed-integer vertex covers on bipartite graphs

By Michele Conforti, Bert Gerards and Giacomo Zambelli

Abstract

Let A be the edge-node incidence matrix of a bipartite graph G = (U,V;E), I be a subset of the nodes of G, and b be a vector such that 2b is integral. We consider the following mixed-integer set: We characterize conv(X(G,b,I)) in its original space. That is, we describe a matrix (C,d) such that conv(X(G,b,I)) = {x : Cx ≥ d}. This is accomplished by computing the projection onto the space of the x-variables of an extended formulation, given in [1], for conv(X(G,b,I)). We then give a polynomial-time algorithm for the separation problem for conv(X(G,b,I)), thus showing that the problem of optimizing a linear function over the set X(G,b,I) is solvable in polynomial time

Topics: Q Science (General), QA Mathematics
Publisher: Springer
Year: 2007
DOI identifier: 10.1007/978-3-540-72792-7_25
OAI identifier: oai:eprints.lse.ac.uk:31690
Provided by: LSE Research Online
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