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A Clique Search Problem and its Application to Machine Scheduling

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  • Sándor Szabó

    (University of Pécs)

Abstract

The paper proposes a new type of clique problem, namely the maximum weight clique problem with predefined coloring. Given a graph with weighted and k-colored nodes, the objective is to find a maximum weight k-clique. As an application it will be shown that a classical single machine scheduling problem can be reduced to this clique problem working with an underlying job conflict graph. Some preprocessing (or kernelization) techniques are also advanced to reduce the size of the graph. In the absence of theoretical tools, numerical experiments evaluate the performance by solving instances derived from moderate size scheduling examples.

Suggested Citation

  • Sándor Szabó, 2021. "A Clique Search Problem and its Application to Machine Scheduling," SN Operations Research Forum, Springer, vol. 2(4), pages 1-12, December.
    • Handle: RePEc:spr:snopef:v:2:y:2021:i:4:d:10.1007_s43069-021-00111-x
    DOI: 10.1007/s43069-021-00111-x
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    References listed on IDEAS

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    1. Egon Balas, 1969. "Machine Sequencing Via Disjunctive Graphs: An Implicit Enumeration Algorithm," Operations Research, INFORMS, vol. 17(6), pages 941-957, December.
    2. 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.
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