Reversed Search Maximum Clique Algorithm Based on Recoloring

  • Deniss KumlanderEmail author
  • Aleksandr Porošin
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)


This work concentrates on finding maximum clique from undirected and unweighted graphs. Maximum clique problem is one of the most known NP-complete problems, the most complex problems of NP class. A lot of other problems can be transformed into clique problem, therefore solving or at least finding a faster algorithm for finding clique will automatically help to solve lots of other tasks. The main contribution of this work is a new exact algorithm for finding maximum clique, which works faster than any currently existing algorithm on a wide variety of graphs. The main idea is to combine a number of efficient improvements from different algorithms into a new one. At first sight these improvements cannot cooperate together, but a new approach of skipping vertices from further expanding instead of pruning the whole branch allows to use all the upgrades at ones. There will be some step-by-step examples with explanations which demonstrate how to use a proposed algorithm.


Graph theory Maximum clique 


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.TalTechTallinnEstonia

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