Blossom V

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 W. Cook and A. Rohe [INFORMS J. Comput. 11, No. 2, 138–148 (1999; Zbl 1040.90539)] 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 [loc. cit.] and K. Mehlhorn and G. Schäfer [ACM J. Exp. Algorithm. 7, Spec. Iss., Article 4, 19 p., electronic only (2002; Zbl 1083.68650)], 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


References in zbMATH (referenced in 24 articles , 1 standard article )

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  1. Fortin, D.: Clustering analysis of a dissimilarity: a review of algebraic and geometric representation (2020)
  2. Dimitrios Michail, Joris Kinable, Barak Naveh, John V Sichi: JGraphT - A Java library for graph data structures and algorithms (2019) arXiv
  3. Pothen, Alex; Ferdous, S. M.; Manne, Fredrik: Approximation algorithms in combinatorial scientific computing (2019)
  4. Dauphinais, Guillaume; Poulin, David: Fault-tolerant quantum error correction for non-abelian anyons (2017)
  5. Genova, Kyle; Williamson, David P.: An experimental evaluation of the best-of-many Christofides’ algorithm for the traveling salesman problem (2017)
  6. Lee, Yi-Chan; Brell, Courtney G.; Flammia, Steven T.: Topological quantum error correction in the Kitaev honeycomb model (2017)
  7. Wøhlk, Sanne; Laporte, Gilbert: Computational comparison of several greedy algorithms for the minimum cost perfect matching problem on large graphs (2017)
  8. Marzouk, Ahmed M.; Moreno-Centeno, Erick; Üster, Halit: A branch-and-price algorithm for solving the Hamiltonian (p)-median problem (2016)
  9. Williamson, Matthew; Eirinakis, Pavlos; Subramani, K.: Fast algorithms for the undirected negative cost cycle detection problem (2016)
  10. Genova, Kyle; Williamson, David P.: An experimental evaluation of the best-of-many Christofides’ algorithm for the traveling salesman problem (2015)
  11. Pereira, André G.; Ritt, Marcus; Buriol, Luciana S.: Optimal Sokoban solving using pattern databases with specific domain knowledge (2015)
  12. Butsch, Alexander; Kalcsics, Jörg; Laporte, Gilbert: Districting for arc routing (2014)
  13. Chishti, Tariq A.; Zhou, Guofei; Pirzada, Shariefuddin; Iványi, Antal: On vertex independence number of uniform hypergraphs (2014)
  14. Wimer, Shmuel: Easy and difficult exact covering problems arising in VLSI power reduction by clock gating (2014)
  15. Wimer, Shmuel; Gluzer, Doron; Wimer, Uri: Using well-solvable minimum cost exact covering for VLSI clock energy minimization (2014)
  16. Stockbridge, Rebecca; Bayraksan, Güzin: A probability metrics approach for reducing the bias of optimality gap estimators in two-stage stochastic linear programming (2013)
  17. Wimer, Shmuel: On optimal flip-flop grouping for VLSI power minimization (2013)
  18. Kirlik, Gokhan; Sipahioglu, Aydin: Capacitated arc routing problem with deadheading demands (2012)
  19. Liers, F.; Pardella, G.: Partitioning planar graphs: a fast combinatorial approach for max-cut (2012)
  20. Bilò, Davide; Forlizzi, Luca; Proietti, Guido: Approximating the metric TSP in linear time (2011)

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