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A new efficient RLF-like algorithm for the vertex coloring problem

Mourchid Adegbindin, Alain Hertz and Martine Bellaïche

Article (2016)

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Abstract

The Recursive Largest First (RLF) algorithm is one of the most popular greedy heuristics for the vertex coloring problem. It sequentially builds color classes on the basis of greedy choices. In particular, the first vertex placed in a color class C is one with a maximum number of uncolored neighbors, and the next vertices placed in C are chosen so that they have as many uncolored neighbors which cannot be placed in C. These greedy choices can have a significant impact on the performance of the algorithm, which explains why we propose alternative selection rules. Computational experiments on 63 difficult DIMACS instances show that the resulting new RLF-like algorithm, when compared with the standard RLF, allows to obtain a reduction of more than 50% of the gap between the number of colors used and the best known upper bound on the chromatic number. The new greedy algorithm even competes with basic metaheuristics for the vertex coloring problem.

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Subjects: 2700 Information technology > 2700 Information technology
2700 Information technology > 2713 Algorithms
2700 Information technology > 2717 Modelling and simulation studies
2950 Applied mathematics > 2956 Optimization and optimal control theory
Department: Department of Computer Engineering and Software Engineering
Department of Mathematics and Industrial Engineering
PolyPublie URL: https://publications.polymtl.ca/3601/
Journal Title: Yugoslav Journal of Operations Research (vol. 26, no. 4)
Publisher: Faculty of Organizational Sciences, Belgrade, Mihajlo Pupin Institute, Belgrade, Faculty of Transport and Traffic Engineering, Belgrade, Faculty of Mining and Geology – Department of Mining, Belgrade, Mathematical Institute SANU, Belgrade
DOI: 10.2298/yjor151102003a
Official URL: https://doi.org/10.2298/yjor151102003a
Date Deposited: 10 Mar 2020 10:32
Last Modified: 29 Apr 2025 11:33
Cite in APA 7: Adegbindin, M., Hertz, A., & Bellaïche, M. (2016). A new efficient RLF-like algorithm for the vertex coloring problem. Yugoslav Journal of Operations Research, 26(4), 441-456. https://doi.org/10.2298/yjor151102003a

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