Exact Algorithms for Maximum Clique: a computational study

We investigate a number of recently reported exact algorithms for the maximum clique problem (MCQ, MCR, MCS, BBMC). The program code used is presented and critiqued showing how small changes in implementation can have a drastic effect on performance. The computational study demonstrates how problem features and hardware platforms influence algorithm behaviour. The minimum width order (smallest-last) is investigated, and MCS is broken into its consituent parts and we discover that one of these parts degrades performance. It is shown that the standard procedure used for rescaling published results is unsafe.