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A fast greedy sequential heuristic for the vertex colouring problem based on bitwise operations

Author

Listed:
  • Larisa Komosko

    (National Research University Higher School of Economics)

  • Mikhail Batsyn

    (National Research University Higher School of Economics)

  • Pablo San Segundo

    (Centre for Automation and Robotics (UPM-CSIC))

  • Panos M. Pardalos

    (National Research University Higher School of Economics
    University of Florida)

Abstract

In this paper a fast greedy sequential heuristic for the vertex colouring problem is presented. The suggested algorithm builds the same colouring of the graph as the well-known greedy sequential heuristic in which on every step the current vertex is coloured in the minimum possible colour. Our main contributions include introduction of a special matrix of forbidden colours and application of efficient bitwise operations on bit representations of the adjacency and forbidden colours matrices. Computational experiments show that in comparison with the classical greedy heuristic the average speedup of the developed approach is 2.6 times on DIMACS instances.

Suggested Citation

  • Larisa Komosko & Mikhail Batsyn & Pablo San Segundo & Panos M. Pardalos, 2016. "A fast greedy sequential heuristic for the vertex colouring problem based on bitwise operations," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1665-1677, May.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:4:d:10.1007_s10878-015-9862-1
    DOI: 10.1007/s10878-015-9862-1
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    References listed on IDEAS

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    1. Mikhail Batsyn & Boris Goldengorin & Evgeny Maslov & Panos M. Pardalos, 2014. "Improvements to MCS algorithm for the maximum clique problem," Journal of Combinatorial Optimization, Springer, vol. 27(2), pages 397-416, February.
    2. Gary Kochenberger & Fred Glover & Bahram Alidaee & Haibo Wang, 2005. "Clustering of Microarray data via Clique Partitioning," Journal of Combinatorial Optimization, Springer, vol. 10(1), pages 77-92, August.
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    Cited by:

    1. Fabio C. S. Dias & Wladimir Araújo Tavares & José Robertty de Freitas Costa, 2020. "Reactive VNS algorithm for the maximum k-subset intersection problem," Journal of Heuristics, Springer, vol. 26(6), pages 913-941, December.
    2. Alejandra Casado & Sergio Pérez-Peló & Jesús Sánchez-Oro & Abraham Duarte, 2022. "A GRASP algorithm with Tabu Search improvement for solving the maximum intersection of k-subsets problem," Journal of Heuristics, Springer, vol. 28(1), pages 121-146, February.

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