Weighted Matching

Part of the Algorithms and Combinatorics book series (AC, volume 21)


Nonbipartite weighted matching appears to be one of the “hardest” combinatorial optimization problems that can be solved in polynomial time. We shall extend Edmonds’ Cardinality Matching Algorithm to the weighted case and shall again obtain an O(n 3)-implementation. This algorithm has many applications, some of which are mentioned in the exercises and in Section 12.2. There are two basic formulations of the weighted matching problem:


Bipartite Graph Perfect Match Dual Solution Incidence Vector Optimum Dual Solution 
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