Simple and Fast: Improving a BranchAndBound Algorithm for Maximum Clique
 Torsten Fahle
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Abstract
We consider a branchandbound algorithm for maximum clique problems. We introduce cost based filtering techniques for the socalled candidate set (i.e. a set of nodes that can possibly extend the clique in the current choice point).
Additionally, we present a taxonomy of upper bounds for maximum clique. Analytical results show that our cost based filtering is in a sense as tight as most of these wellknown bounds for the maximum clique problem.
Experiments demonstrate that the combination of cost based filtering and vertex coloring bounds outperforms the old approach as well as approaches that only apply either of these techniques. Furthermore, the new algorithm is competitive with other recent algorithms for maximum clique.
 Title
 Simple and Fast: Improving a BranchAndBound Algorithm for Maximum Clique
 Book Title
 Algorithms — ESA 2002
 Book Subtitle
 10th Annual European Symposium Rome, Italy, September 17–21, 2002 Proceedings
 Pages
 pp 485498
 Copyright
 2002
 DOI
 10.1007/3540457496_44
 Print ISBN
 9783540441809
 Online ISBN
 9783540457497
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 2461
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 maximum clique
 branchandbound
 constraint programming
 cost based filtering
 Industry Sectors
 eBook Packages
 Editors

 Rolf Möhring ^{(4)}
 Rajeev Raman ^{(5)}
 Editor Affiliations

 4. Fakultät II: Mathematik und Naturwissenschaften, Technische Universität Berlin
 5. Department of Mathematics and Computer Science, University of Leicester
 Authors

 Torsten Fahle ^{(6)}
 Author Affiliations

 6. Department of Mathematics and Computer Science, University of Paderborn, Fürstenallee 11, D33102, Paderborn, Germany
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