Abstract
In this chapter we discuss the problem of constructing a min-cost perfect matching in general graphs. We have introduced 1MP as an integer program using the node-edge incidence matrix A. In the bipartite case we could show that A is totally unimodular and hence AP can be solved by solving the LP-relaxation of the integer program. This approach is not possible for nonbipartite graphs since the polytope associated with the LP-relaxation may have fractional vertices. Thus before discussing different algorithmic principles, we first establish the so-called matching polytope, i.e. the polyhedron the vertices of which correspond to matchings in G.
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© 1988 Springer-Verlag Berlin Heidelberg
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Derigs, U. (1988). The Min-Cost Perfect Matching Problem. In: Programming in Networks and Graphs. Lecture Notes in Economics and Mathematical Systems, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51713-6_13
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DOI: https://doi.org/10.1007/978-3-642-51713-6_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18969-5
Online ISBN: 978-3-642-51713-6
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