Abstract
We describe the implementation of an O(nmlog n) algorithm for weighted matchings in general graphs. The algorithm is a variant of the algorithm of Galil, Micali, and Gabow [12] and requires the use of concatenable priority queues. No previous implementation had a worst-case guarantee of O(nmlog n). We compare our implementation to the experimentally fastest implementation (called Blossom IV) due to Cook and Rohe [4]; Blossom IV is an implementation of Edmonds’ algorithm and has a running time no better than (n3). Blossom IV requires only very simple data structures. Our experiments show that our new implementation is competitive to Blossom IV.
The maximum-weight matching problem can be reduced to the maximum-weight perfect matching problem: the original graph is doubled and zero weight edges are inserted from each original vertex to the corresponding doubled vertex. For an original graph with n vertices and m edges, the reduction doubles n and increases m by m + n; it soon becomes impractical for large instances.
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Mehlhorn, K., Schäfer, G. (2001). Implementation of O(nmlog n) Weighted Matchings in General Graphs. The Power of Data Structures. In: Näher, S., Wagner, D. (eds) Algorithm Engineering. WAE 2000. Lecture Notes in Computer Science, vol 1982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44691-5_3
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DOI: https://doi.org/10.1007/3-540-44691-5_3
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