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The minimum weight dominating set (MWDS) problem is NP-hard and also important in many applications. Recent heuristic MWDS algorithms can hardly solve massive real world graphs effectively. In this paper, we design a fast local search algorithm called FastMWDS for the MWDS problem, which aims to obtain a good solution on massive graphs within a short time. In this novel local search framework, we propose two ideas to make it effective. Firstly, we design a new fast construction procedure with four reduction rules to cut down the size of massive graphs. Secondly, we propose the three-valued two-level configuration checking strategy to improve local search, which is interestingly a variant of configuration checking (CC) with two levels and multiple values. Experiment results on a broad range of massive real world graphs show that FastMWDS finds much better solutions than state of the art MWDS algorithms.

The set k‐covering problem (SKCP) is NP‐hard and has important real‐world applications. In this paper, we propose several improvements over typical algorithms for its solution. First, we present a multilevel (ML) score heuristic that reflects relevant information of the currently selected subsets inside or outside a candidate solution. Next, we propose QCC to overcome the cycling problem in local search. Based on the ML heuristic and QCC strategy, we propose an effective subset selection strategy. Then, we integrate these methods into a local search algorithm, which we called MLQCC. In addition, we propose a preprocessing method to reduce the scale of the original problem before applying MLQCC. We further enhance MLQCC for large‐scale instances using a low‐time‐complexity initialization algorithm to determine an initial candidate solution, obtaining the MLQCC + LI algorithm. The performance of the proposed MLQCC and MLQCC + LI is verified through experimental evaluations on both classical and large‐scale benchmarks. The results show that MLQCC and MLQCC + LI notably outperform several state‐of‐the‐art SKCP algorithms on the evaluated benchmarks.

The maximum k-plex, a generalization of maximum clique, is used to cope with a great number of real-world problems. The aim of this paper is to propose a novel exact k-plex algorithm that can deal with large-scaled graphs with millions of vertices and edges. Specifically, we first propose several new graph reduction methods through a careful analyzing of structures of induced subgraphs. Afterwards, we present a preprocessing method to simplify initial graphs. Additionally, we present a branch-and-bound algorithm integrating the reduction methods as well as a new dynamic vertex selection mechanism. We perform intensive experiments to evaluate our algorithm, and show that the proposed strategies are effective and our algorithm outperforms state-of-the-art algorithms, especially for real-world massive graphs.