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Mixed-integer vertex covers on bipartite graphs

Conforti, Michele, Gerards, Bert and Zambelli, Giacomo (2007) Mixed-integer vertex covers on bipartite graphs. In: Fischetti, Matteo and Williamson, David .P., (eds.) Integer Programming and Combinatorial Optimization. Lecture notes in computer science (4513). Springer, Berlin, Germany, pp. 324-336. ISBN 9783540727927

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Identification Number: 10.1007/978-3-540-72792-7_25


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.

Item Type: Book Section
Official URL:
Additional Information: © 2007 Springer-Verlag Berlin Heidelberg
Divisions: Management
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Date Deposited: 25 Jan 2011 13:53
Last Modified: 20 May 2021 01:25
Projects: 12th International IPCO Conference, Ithaca, NY, USA

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