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Weighted maximum matching in general graphs

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Computes a maximum-weighted matching in a general undirected graph.



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Computes a maximum-weighted matching in a general undirected graph. There is the option to only consider maximum-cardinality matching.
Originally written by Joris van Rantwijk in Python:

Ported to MATLAB, with permission (and not optimized, e.g. for modularity), by Daniel R. Saunders, 2013. BSD license. Original header follows:

The algorithm is taken from "Efficient Algorithms for Finding Maximum Matching in Graphs" by Zvi Galil, ACM Computing Surveys, 1986. It is based on the "blossom" method for finding augmenting paths and the "primal-dual" method for finding a matching of maximum weight, both due to Jack Edmonds.
Some ideas came from "Implementation of algorithms for maximum matching on non-bipartite graphs" by H.J. Gabow, Standford Ph.D. thesis, 1973.

A C program for maximum weight matching by Ed Rothberg was used extensively to validate this new code.

Comments and Ratings (2)

HyoJoon Park

How should I interpret the outcome of:
edgeData = [2, 3, 10; 3, 4, 11]
result = maxWeightMatching(edgeData)

which is [-1 -1 4 3]?

but it show me there is error , i am using matlab 2015a


Fixed a bug that caused certain test cases to return suboptimal matches. Thanks to Jan and to Francesco Betti Sorbelli!

MATLAB Release Compatibility
Created with R2008b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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