Facets of an Assignment Problem with 0–1 Side Constraint

Abdo Y. Alfakih (), Tongnyoul Yi and Katta G. Murty ()
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Abdo Y. Alfakih: University of Michigan
Tongnyoul Yi: Samsung Data Systems
Katta G. Murty: University of Michigan

Journal of Combinatorial Optimization, 2000, vol. 4, issue 3, No 5, 365-388

Abstract: Abstract We show that the problem of finding a perfect matching satisfying a single equality constraint with a 0–1 coefficients in an n × n incomplete bipartite graph, polynomially reduces to a special case of the same peoblem called the partitioned case. Finding a solution matching for the partitioned case in the incomlpete bipartite graph, is equivalent to minimizing a partial sum of the variables over $$Q_{n_{1,} n_2 }^{n,r_1 } $$ = the convex hull of incidence vectors of solution matchings for the partitioned case in the complete bipartite graph. An important strategy to solve this minimization problem is to develop a polyhedral characterization of $$Q_{n_{1,} n_2 }^{n,r_1 } $$ . Towards this effort, we present two large classes of valid inequalities for $$Q_{n_{1,} n_2 }^{n,r_1 } $$ , which are proved to be facet inducing using a facet lifting scheme.

Keywords: constrained assignment problem; integer hull; facet inducing inequalities; facet lifting scheme (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1009878328812

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