Artificial Intelligence Review

, Volume 47, Issue 3, pp 367–394 | Cite as

Algorithms for the minimum sum coloring problem: a review

  • Yan Jin
  • Jean-Philippe Hamiez
  • Jin-Kao Hao


The minimum sum coloring problem (MSCP) is a variant of the well-known vertex coloring problem which has a number of AI related applications. Due to its theoretical and practical relevance, MSCP attracts increasing attention. The only existing review on the problem dates back to 2004 and mainly covers the history of MSCP and theoretical developments on specific graphs. In recent years, the field has witnessed significant progresses on approximation algorithms and practical solution algorithms. The purpose of this review is to provide a comprehensive inspection of the most recent and representative MSCP algorithms. To be informative, we identify the general framework followed by practical solution algorithms and the key ingredients that make them successful. By classifying the main search strategies and putting forward the critical elements of the reviewed methods, we wish to encourage future development of more powerful methods and motivate new applications.


Sum coloring Approximation algorithms Heuristics and metaheuristics Local search Evolutionary algorithms 



We are grateful to the anonymous referees for valuable suggestions and comments which have helped us to improve the paper. This work was partially supported by the LigeRO (2009–2014, Pays de la Loire Region), PGMO (2014–2016, Jacques Hadamard Mathematical Foundation) projects and the National Natural Science Foundation Program of China (Grant No. 61472147).


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyHuazhong University of Science and TechnologyWuhanChina
  2. 2.LERIAUniversité d’AngersAngersFrance
  3. 3.Institut Universitaire de FranceParisFrance

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