Reactive and dynamic local search for max-clique: Engineering effective building blocks

This paper presents the results of an ongoing investigation about how different algorithmic building blocks contribute to solving the maximum clique problem. We consider greedy constructions, plateau searches, and more complex schemes based on dynamic penalties and/or prohibitions, in particular the recently proposed technique of dynamic local search and the previously proposed reactive local search (RLS). We design a variation of the original RLS algorithm where the role of long-term memory (LTM) is increased (RLS-LTM). In addition, we consider in detail the effect of the low-level implementation choices on the CPU time per iteration. We present experimental results on randomly generated graphs with different statistical properties, showing the crucial effects of the implementation, the robustness of different techniques, and their empirical scalability.