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IPCO
2007

Mixed-Integer Vertex Covers on Bipartite Graphs

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Mixed-Integer Vertex Covers on Bipartite Graphs
Let A be the edge-node incidence matrix of a bipartite graph G = (U, V ; E), I be a subset the nodes of G, and b be a vector such that 2b is integral. We consider the following mixed-integer set: X(G, b, I) = {x : Ax ≥ b, x ≥ 0, xi integer for all i ∈ I}. We characterize conv(X(G, b, I)) in its original space. That is, we describe a matrix (A , b ) such that conv(X(G, b, I)) = {x : A x ≥ b }. 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 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 polynomially solvable.
Michele Conforti, Bert Gerards, Giacomo Zambelli
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2007
Where IPCO
Authors Michele Conforti, Bert Gerards, Giacomo Zambelli
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