Matchings in colored bipartite networks

In K(n, n) with edges colored either red or blue, we show that the problem of finding a solution matching, a perfect matching consisting of exactly r red edges, and (n - r) blue edges for specified 0 r n, is a nontrivial integer program. We present an alternative, logically simpler proof of a theorem in [3] which establishes necessary and sufficient conditions for the existance of a solution matching and a new O(n2.5) algorithm. This shows that the problem of finding an assignment of specified cost r in an assignment problem on the complete bipartite graph with a 0-1 cost matrix is efficiently solvable. Key words assignment problem, 0-1 cost matrix, extreme point with specified objective value. +Author for correspondence 1 

• Type: Journal
• Year: 2002
• Where: DAM
• Authors: Tongnyoul Yi, Katta G. Murty, Cosimo Spera
• Keywords: Assignment Problem, Blue Edges, DAM 2002, Nontrivial Integer Program