A Clique Search Problem and its Application to Machine Scheduling

Sándor Szabó
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Sándor Szabó: University of Pécs

SN Operations Research Forum, 2021, vol. 2, issue 4, 1-12

Abstract: 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.

Keywords: Combinatorial optimization; Clique and chromatic numbers; Weighted maximum clique; Practical solutions of NP-complete problems; Primary 94B60; Secondary 05B45; 52C22 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s43069-021-00111-x

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