Blossom V: a new implementation of a minimum cost perfect matching algorithm

  • We describe a new implementation of the Edmonds’s algorithm for computing a perfect matching of minimum cost, to which we refer as Blossom V. A key feature of our implementation is a combination of two ideas that were shown to be effective for this problem: the “variable dual updates” approach of Cook and Rohe (INFORMS J Comput 11(2):138–148, 1999) and the use of priority queues. We achieve this by maintaining an auxiliary graph whose nodes correspond to alternating trees in the Edmonds’s algorithm. While our use of priority queues does not improve the worst-case complexity, it appears to lead to an efficient technique. In the majority of our tests Blossom V outperformed previous implementations of Cook and Rohe (INFORMS J Comput 11(2):138–148, 1999) and Mehlhorn and Schäfer (J Algorithmics Exp (JEA) 7:4, 2002), sometimes by an order of magnitude. We also show that for large VLSI instances it is beneficial to update duals by solving a linear program, contrary to a conjecture by Cook and Rohe.

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Metadaten
Author:Vladimir Kolmogorov
DOI:https://doi.org/10.1007/s12532-009-0002-8
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2009
Tag:Software; Theoretical Computer Science
Volume:1
Issue:1
Page Number:25
First Page:43
Last Page:67
Mathematical Programming Computation :MPC 2009 - Issue 1
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