Abstract
Diversified top-k weight clique (DTKWC) search problem is an important generalization of the diversified top-k clique (DTKC) search problem with practical applications. The diversified top-k weight clique search problem aims to search k maximal cliques that can cover the maximum weight in a vertex weighted graph. In this work, we propose a novel local search algorithm called TOPKWCLQ for the DTKWC search problem which mainly includes two strategies. First, a restart strategy is adopted, which repeated the construction and updating processes of the maximal weight clique set. Second, a scoring heuristic is designed by giving different priorities for maximal weight cliques in candidate set. Meanwhile, a constraint model of the DTKWC search problem is constructed such that the research concerns can be evaluated. Experimental results show that the proposed algorithm TOPKWCLQ outperforms than the comparison algorithm on large-scale real-world graphs.
Highlights
Local Search for Solving DiversifiedGiven an undirected graph G = (V, E), a clique is a subset of the graph G, where any two vertices are adjacent
Since there is no suitable heuristic or exact algorithm for the diversified top-k weight clique (DTKWC) search problem on real-world large graphs in literature, as we know that is a good choice to compare the results of the proposed algorithm to the results obtained by CPLEX solver which is a commercial solver for many combinatorial optimization problems with their constraint formulas of mathematical models
In TOPKWCLQ, we present the maximum weight value of the DTKWC search problem instances and the average weight DTKWC search problem results obtained over
Summary
Zhou et al [1] (2021) encode the DTKWC search problem into the weighted partial MaxSAT (WPMS) problem, including direct encoding (DE) and independent set partition based encoding (ISPE), and solving WPMS with state-of-the-art solvers This method is limited to solve real-world large graphs, because it is failed to encode large graphs into WPMS. We propose a local search algorithm for the DTKWC search problem in large graphs, which provides a local optimal solution within a reasonable time and avoids the generation and storage of all maximal weight cliques. It aims at addressing the aforementioned problem.
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