Local search for diversified Top-k clique search problem

The objective of the diversified top-k clique (DTKC) search problem is to find k maximal cliques that cover the maximum number of vertices in a given graph. This problem is equivalent to the well-known maximum clique problem (MaxClique) when k = 1. This paper proves the NP-hardness of the DTKC search problem and presents a local search algorithm, named TOPKLS, based on two novel strategies for the DTKC search problem. The first strategy is called enhanced configuration checking (ECC), which is a new variant of a recent effective strategy called configuration checking (CC), for reducing cycling in the local search and improving the diversity of the DTKC search problem. The second strategy is a heuristic to estimate the quality of each maximal clique. Experiments demonstrate that TOPKLS outperforms the existing algorithms on large sparse graphs from real-world applications. (C) 2019 Elsevier Ltd. All rights reserved.