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Minimizing cyclic cutwidth of graphs using a memetic algorithm

Author

Listed:
  • Pallavi Jain

    (Dayalbagh Educational Institute)

  • Kamal Srivastava

    (Dayalbagh Educational Institute)

  • Gur Saran

    (Dayalbagh Educational Institute)

Abstract

Cyclic cutwidth minimization problem (CCMP) consists of embedding a graph onto a circle such that the maximum cutwidth in a region is minimized. It is an NP-complete problem and for some classes of graphs, exact results of cyclic cutwidth have been proved in literature. However, no algorithm has been reported for general graphs. In this paper, a memetic algorithm is proposed for CCMP in which we have designed six construction heuristics in order to generate a good initial population and also local search is employed to improve the solutions in each generational phase. The algorithm achieves optimal results for the classes of graphs with known exact results. Extensive experiments have also been conducted on some classes of graphs for which exact results are not known such as the complete split graph, join of hypercubes, toroidal meshes, cone graph and some instances of Harwell-Boeing graphs which are a subset of public domain Matrix Market library. Trends observed in the experimental results for some of the classes of graphs have led to conjectures for cyclic cutwidth.

Suggested Citation

  • Pallavi Jain & Kamal Srivastava & Gur Saran, 2016. "Minimizing cyclic cutwidth of graphs using a memetic algorithm," Journal of Heuristics, Springer, vol. 22(6), pages 815-848, December.
    • Handle: RePEc:spr:joheur:v:22:y:2016:i:6:d:10.1007_s10732-016-9319-4
    DOI: 10.1007/s10732-016-9319-4
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    References listed on IDEAS

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    1. Juan Pantrigo & Rafael Martí & Abraham Duarte & Eduardo Pardo, 2012. "Scatter search for the cutwidth minimization problem," Annals of Operations Research, Springer, vol. 199(1), pages 285-304, October.
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    Cited by:

    1. Sergio Cavero & Eduardo G. Pardo & Abraham Duarte, 2022. "A general variable neighborhood search for the cyclic antibandwidth problem," Computational Optimization and Applications, Springer, vol. 81(2), pages 657-687, March.
    2. Mu He & Qinghua Wu & Yongliang Lu, 2022. "Breakout local search for the cyclic cutwidth minimization problem," Journal of Heuristics, Springer, vol. 28(5), pages 583-618, December.

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