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 (4513). Springer, Berlin, Germany, pp. 324-336. ISBN 9783540727927
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.
| Item Type: | Book Section |
|---|---|
| Official URL: | http://www.informatik.uni-trier.de/~ley/db/conf/ip... |
| Additional Information: | © 2007 Springer-Verlag Berlin Heidelberg |
| Library of Congress subject classification: | Q Science > Q Science (General) Q Science > QA Mathematics |
| Sets: | Departments > Management |
| Rights: | http://www.lse.ac.uk/library/rights/LSERO.htm |
| URL: | http://eprints.lse.ac.uk/31690/ |
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