Open Access

Branch and bound algorithms for the maximum clique problem under a unified framework

Journal of the Brazilian Computer Society201118:50

https://doi.org/10.1007/s13173-011-0050-6

Received: 14 November 2011

Accepted: 23 November 2011

Published: 24 December 2011

Abstract

In this paper we review branch and bound-based algorithms proposed for the exact solution of the maximum clique problem and describe them under a unifying conceptual framework. As a proof of concept, we actually implemented eight of these algorithms as parametrized versions of one single general branch and bound algorithm.

The purpose of the present work is double folded. In the one hand, the implementation of several different algorithms under the same computational environment allows for a more precise assessment of their comparative performance at the experimental level. On the other hand we see the unifying conceptual framework provided by such description as a valuable step toward a more fine grained analysis of these algorithms.

Keywords

Maximum clique Exact solution Branch and bound