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One-Half Approximation Algorithms for the k-Partition Problem

Author

Listed:
  • Thomas Feo

    (The University of Texas at Austin, Austin, Texas)

  • Olivier Goldschmidt

    (The University of Texas at Austin, Austin, Texas)

  • Mallek Khellaf

    (British Telecom Tymnet, Paris, France)

Abstract

The k -partition problem seeks to cluster the vertices of an edge-weighted graph, G = ( V , E ), into k sets of | V |/ k vertices each, such that the total weight of the edges having both endpoints in the same cluster is maximized. Bottom-up type heuristics based on matchings are presented for this problem. These heuristics are shown to yield solutions that are at least one-half the weight of the optimal solution for k equal to | V |/3 and | V |/4.

Suggested Citation

  • Thomas Feo & Olivier Goldschmidt & Mallek Khellaf, 1992. "One-Half Approximation Algorithms for the k-Partition Problem," Operations Research, INFORMS, vol. 40(1-supplem), pages 170-173, February.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:1-supplement-1:p:s170-s173
    DOI: 10.1287/opre.40.1.S170
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    Citations

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    Cited by:

    1. Esther M. Arkin & Refael Hassin, 1998. "On Local Search for Weighted k -Set Packing," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 640-648, August.
    2. Z P Fan & Y Chen & J Ma & S Zeng, 2011. "A hybrid genetic algorithmic approach to the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 92-99, January.
    3. Baoling Ning & Jianzhong Li & Shouxu Jiang, 2019. "Balanced tree partition problems with virtual nodes," Journal of Combinatorial Optimization, Springer, vol. 37(4), pages 1249-1265, May.
    4. Z P Fan & Y Chen & J Ma & S Zeng, 2011. "Erratum: A hybrid genetic algorithmic approach to the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1423-1430, July.
    5. Weitz, R. R. & Lakshminarayanan, S., 1997. "An empirical comparison of heuristic and graph theoretic methods for creating maximally diverse groups, VLSI design, and exam scheduling," Omega, Elsevier, vol. 25(4), pages 473-482, August.
    6. Chenchen Wu & Dachuan Xu & Donglei Du & Wenqing Xu, 2016. "An approximation algorithm for the balanced Max-3-Uncut problem using complex semidefinite programming rounding," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1017-1035, November.
    7. Anna Martínez-Gavara & Vicente Campos & Micael Gallego & Manuel Laguna & Rafael Martí, 2015. "Tabu search and GRASP for the capacitated clustering problem," Computational Optimization and Applications, Springer, vol. 62(2), pages 589-607, November.
    8. Kayse Lee Maass & Vera Mann Hey Lo & Anna Weiss & Mark S. Daskin, 2015. "Maximizing Diversity in the Engineering Global Leadership Cultural Families," Interfaces, INFORMS, vol. 45(4), pages 293-304, August.

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