Chapter

Algorithms — ESA 2002

Volume 2461 of the series Lecture Notes in Computer Science pp 485-498

Date:

Simple and Fast: Improving a Branch-And-Bound Algorithm for Maximum Clique

  • Torsten FahleAffiliated withDepartment of Mathematics and Computer Science, University of Paderborn

* Final gross prices may vary according to local VAT.

Get Access

Abstract

We consider a branch-and-bound 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 well-known 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.

Keywords

maximum clique branch-and-bound constraint programming cost based filtering