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Heuristic methods for graph coloring problems

Published: 13 March 2005 Publication History

Abstract

In this work, the Graph Coloring Problem and its generalizations - the Bandwidth Coloring Problem, the Multicoloring Problem and the Bandwidth Multicoloring Problem - are studied. A Squeaky Wheel Optimization with Tabu Search heuristic is developed and experiments using benchmark geometric test cases show that the algorithm performs well for these problems and achieves results for the Bandwidth Multicoloring Problem which improve on results obtained by other researchers.

References

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David P. Clements, James M. Crawford, David E. Joslin, Geoge L. Nemhauser, Markus E. Puttlitz, and Martin W. P. Savelsbergh. Heurstic optimization: A hybrid ai/or approach. In Proceedings of the Workshop on Industrial Constraint-Directed Scheduling, 1997.
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Joseph C. Culberson and Feng Luo. Exploring the k-colorable landscape with iterative greedy. Cliques, Coloring and Satisfiability, Second DIMACS Implementation Challenge, 1993.
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Fred Glover and Manuel Laguna. Tabu Search. Kluwer Acadamic Publishers, 1997.
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Fred Glover, Mark Parker, and Jennifer Ryan. Coloring by tabu branch and bound. Cliques, Coloring and Satisfiability, Second DIMACS Implementation Challenge, 1993.
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A. Hertz and D. de Werra. Using tabu search techniques for graph coloring. Computing, 39:345--351, 1987.
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D. S. Johnson, C. A. Aragon, L. A. Mcgeoch, and C. Schevon. Optimization by simulated annealing: An experimental evaluation c part ii (graph coloring and number partitioning). Operations Research, 31:378--406, 1991.
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David S. Johnson and Michael A. Trick (Editors). Cliques, Coloring and Satisfiability, Second DIMACS Implementation Challenge. American Mathematical Society, 1993.
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David E. Joslin and David P. Clements, "squeaky wheel" optimization. In Proceedings of American Association of Artificial Intelligence National Conference 1998, pages 340--346, 1998.
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Gray Lewandowski and Anne Condon. Expreiments with parallel graph coloring heuristics and applications of graph coloring. Cliques, Coloring and Satisfiability, Second DIMACS Implementation Challenge, 1993.
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Andrew Lim, Brian Rodrigues, and Yi Zhu. Crane scheduling using swo with local search. In Proceedings of 4th Asia-Pacific Conference on Simulated Evolution and Learning, 2002.
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Andrew Lim, Xingwen Zhang, and Yi Zhu. A hybrid method for the graph coloring problem and its generalizations. In 5th Metaheuristics International Conference (MIC 2003), 2002.
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Craig Morgenstern. Distributed coloration neighborhood search. Cliques, Coloring and Satisfiability, Second DIMACS Implementation Challenge, 1993.
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Eun-Jon Park, Yong-Hyuk Kim, and Byung-Ro Moon. Genetic search for fixed channel assignment problem with limited bandwidth. In Proceedings of Genetic and Evolutionary Computation Conference, pages 1772--1779, 2002.
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Steven Prestwich. Constrained bandwidth multicoloration neighborhoods. In Proceedings of Computational Symposium on Graph Coloring and its Generalizations, 2002.
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E. C. Sewell. An improved algorithm for exact graph coloring. Cliques, Coloring and Satisfiability, Second DIMACS Implementation Challenge, 1993.

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  • (2023)Effective implementation of the High Performance Conjugate Gradient benchmark on GraphBLAS2023 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)10.1109/IPDPSW59300.2023.00044(216-225)Online publication date: May-2023
  • (2019)DIAMOND: a distributed algorithm for vertex coloring problems and resource allocationIET Networks10.1049/iet-net.2018.52048:6(381-389)Online publication date: Nov-2019
  • (2017)Event-driven data aggregation and reporting for CRSN-based substation monitoring2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC)10.1109/PIMRC.2017.8292539(1-7)Online publication date: Oct-2017
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    cover image ACM Conferences
    SAC '05: Proceedings of the 2005 ACM symposium on Applied computing
    March 2005
    1814 pages
    ISBN:1581139640
    DOI:10.1145/1066677
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 13 March 2005

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    Author Tags

    1. graph coloring
    2. heuristics
    3. optimization
    4. tabu search

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    SAC05: The 2005 ACM Symposium on Applied Computing
    March 13 - 17, 2005
    New Mexico, Santa Fe

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    Overall Acceptance Rate 1,650 of 6,669 submissions, 25%

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    Cited By

    View all
    • (2023)Effective implementation of the High Performance Conjugate Gradient benchmark on GraphBLAS2023 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)10.1109/IPDPSW59300.2023.00044(216-225)Online publication date: May-2023
    • (2019)DIAMOND: a distributed algorithm for vertex coloring problems and resource allocationIET Networks10.1049/iet-net.2018.52048:6(381-389)Online publication date: Nov-2019
    • (2017)Event-driven data aggregation and reporting for CRSN-based substation monitoring2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC)10.1109/PIMRC.2017.8292539(1-7)Online publication date: Oct-2017
    • (2016)Makespan minimisation for a parallel machine scheduling problem with preemption and job incompatibilityInternational Journal of Production Research10.1080/00207543.2016.118128555:6(1588-1606)Online publication date: 8-May-2016
    • (2016)A learning-based path relinking algorithm for the bandwidth coloring problemEngineering Applications of Artificial Intelligence10.1016/j.engappai.2016.02.00852:C(81-91)Online publication date: 1-Jun-2016
    • (2016)Control Synthesis and Pin-Count MinimizationMicrofluidic Very Large Scale Integration (VLSI)10.1007/978-3-319-29599-2_7(111-124)Online publication date: 9-Feb-2016
    • (2015)A learning approach to the bandwidth multicolouring problemJournal of Experimental & Theoretical Artificial Intelligence10.1080/0952813X.2015.101521828:3(499-527)Online publication date: 5-May-2015
    • (2013)Memetic Algorithm to Solve Graph Coloring ProblemInternational Journal of Computer Theory and Engineering10.7763/IJCTE.2013.V5.817(890-894)Online publication date: 2013
    • (2013)Control synthesis for the flow-based microfluidic large-scale integration biochips2013 18th Asia and South Pacific Design Automation Conference (ASP-DAC)10.1109/ASPDAC.2013.6509597(205-212)Online publication date: Jan-2013
    • (2013)Multistart Iterated Tabu Search for Bandwidth Coloring ProblemComputers and Operations Research10.1016/j.cor.2012.09.00340:5(1401-1409)Online publication date: 1-May-2013
    • Show More Cited By

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