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Computing MinimumWeight Perfect Matchings
 INFORMS
, 1999
"... We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the ..."
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Cited by 90 (2 self)
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We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimumweight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the use of multiple search trees with an individual dualchange � for each tree. As a benchmark of the algorithm’s performance, solving a 100,000node geometric instance on a 200 Mhz PentiumPro computer takes approximately 3 minutes.
Implementation of O(nm log n) Weighted Matchings in General Graphs  The Power of Data Structures
 IN WORKSHOP ON ALGORITHM ENGINEERING (WAE), LECTURE NOTES IN COMPUTER SCIENCE
, 2000
"... We describe the implementation of an O(nm log n) algorithm for weighted matchings in general graphs. The algorithm is a variant of the algorithm of Galil, Micali, and Gabow [GMG86] and requires the use of concatenable priority queues. No previous implementation had a worst{case guarantee of O(nm ..."
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Cited by 7 (1 self)
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We describe the implementation of an O(nm log n) algorithm for weighted matchings in general graphs. The algorithm is a variant of the algorithm of Galil, Micali, and Gabow [GMG86] and requires the use of concatenable priority queues. No previous implementation had a worst{case guarantee of O(nm log n). We compare our implementation to the experimentally fastest implementation (called Blossom IV) due to Cook and Rohe [CR97]; Blossom IV is an implementation of Edmonds' algorithm and has a running time no better than Ω(n³). Blossom IV requires only very simple data structures. Our experiments show that our new implementation is competitive to Blossom IV.
DOI 10.1007/s1253200900028 FULL LENGTH PAPER
"... Abstract 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 ” appr ..."
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Abstract 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 worstcase 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.
Polynomial Algorithms for Item Matching
, 1992
"... To estimate test reliability and to create parallel tests, test items frequently are matched. Items can be matched by splitting tests into parallel test halves, by creating T splits, or by matching a desired test form. Problems often occur. Algorithms are presented to solve these problems. The algor ..."
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To estimate test reliability and to create parallel tests, test items frequently are matched. Items can be matched by splitting tests into parallel test halves, by creating T splits, or by matching a desired test form. Problems often occur. Algorithms are presented to solve these problems. The algorithms are based on optimization theory in networks (graphs) and have polynomial complexity. Computational results from solving sample problems with several hundred decision variables are reported. Index terms: branchandbound algorithm, classical test theory, complexity, item matching, nondeterministic polynomial complete, parallel tests, polynomial algorithms, test construction. Gulliksen (1950/1987) presented a matching