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Multiple Hungarian Method for k -Assignment Problem

Author

Listed:
  • Boštjan Gabrovšek

    (Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, SI-1000 Ljubljana, Slovenia
    Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia)

  • Tina Novak

    (Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, SI-1000 Ljubljana, Slovenia)

  • Janez Povh

    (Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, SI-1000 Ljubljana, Slovenia
    Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia)

  • Darja Rupnik Poklukar

    (Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, SI-1000 Ljubljana, Slovenia)

  • Janez Žerovnik

    (Faculty of Mechanical Engineering, University of Ljubljana, Askerceva 6, SI-1000 Ljubljana, Slovenia
    Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia)

Abstract

The k -assignment problem (or, the k -matching problem) on k -partite graphs is an NP-hard problem for k ≥ 3 . In this paper we introduce five new heuristics. Two algorithms, B m and C m , arise as natural improvements of Algorithm A m from (He et al., in: Graph Algorithms And Applications 2, World Scientific, 2004). The other three algorithms, D m , E m , and F m , incorporate randomization. Algorithm D m can be considered as a greedy version of B m , whereas E m and F m are versions of local search algorithm, specialized for the k -matching problem. The algorithms are implemented in Python and are run on three datasets. On the datasets available, all the algorithms clearly outperform Algorithm A m in terms of solution quality. On the first dataset with known optimal values the average relative error ranges from 1.47% over optimum (algorithm A m ) to 0.08% over optimum (algorithm E m ). On the second dataset with known optimal values the average relative error ranges from 4.41% over optimum (algorithm A m ) to 0.45% over optimum (algorithm F m ). Better quality of solutions demands higher computation times, thus the new algorithms provide a good compromise between quality of solutions and computation time.

Suggested Citation

  • Boštjan Gabrovšek & Tina Novak & Janez Povh & Darja Rupnik Poklukar & Janez Žerovnik, 2020. "Multiple Hungarian Method for k -Assignment Problem," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2050-:d:446526
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    References listed on IDEAS

    as
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