A Dual-mode Local Search Algorithm for Solving the Minimum Dominating Set Problem

作     者：Zhu, Enqiang Zhang, Yu Wang, Shengzhi Strash, Darren Liu, Chanjuan 

作者机构：Institute of Computing Science and Technology Guangzhou University Guangzhou510006 China Cyberspace Institute of Advanced Technology Guangzhou University Guangzhou510006 China Department of Computer Science Hamilton College ClintonNY13323 United States School of Computer Science and Technology Dalian University of Technology Dalian116024 China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2023年

核心收录：

主　　题：Heuristic algorithms 

摘      要：Given a graph, the minimum dominating set (MinDS) problem is to identify a smallest set D of vertices such that every vertex not in D is adjacent to at least one vertex in D. The MinDS problem is a classic NP-hard problem and has been extensively studied because of its many disparate applications in network analysis. To solve this problem efficiently, many heuristic approaches have been proposed to obtain a good solution within an acceptable time limit. However, existing MinDS heuristic algorithms are always limited by various tie-breaking cases when selecting vertices, which slows down the effectiveness of the algorithms. In this paper, we design an efficient local search algorithm for the MinDS problem, named DmDS—a dual-mode local search framework that probabilistically chooses between two distinct vertex-swapping schemes. We further address limitations of other algorithms by introducing vertex selection criterion based on the frequency of vertices added to solutions to address tie-breaking cases, and a new strategy to improve the quality of the initial solution via a greedy-based strategy integrated with perturbation. We evaluate DmDS against the state-of-the-art algorithms on seven datasets, consisting of 346 instances (or families) with up to tens of millions of vertices. Experimental results show that DmDS obtains the best performance in accuracy for almost all instances and finds much better solutions than state-of-the-art MinDS algorithms on a broad range of large real-world graphs. Copyright © 2023, The Authors. All rights reserved.