An Efficient Local Search Algorithm for the Minimum <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-Dominating Set Problem

Abstract

The minimum $k$ -dominating set (MKDS) problem, a generalization of the classical minimum dominating set problem, is an important NP-hard combinatorial optimization problem with various applications. First, to alleviate the cycling problem in the local search, a MKDS two-level configuration checking (MKDSCC2) strategy is presented. Second, we use the vertex cost scheme to define the scoring mechanism and to improve the solution effectively. Third, by combining MKDSCC2 strategy and the scoring mechanism, we propose a vertex selection strategy to decide which vertex should be added into or removed from the candidate solution. Based on these strategies, an efficient local search algorithm (VSCC2), which incorporates a two-level configuration checking strategy, scoring mechanism, and vertex selection strategy, is proposed. We compare the performance of VSCC2 with the classic GRASP algorithm and the famous commercial solver CPLEX on the classical instances. The comprehensive results show that the VSCC2 algorithm is very competitive in terms of solution quality and computing time.

Keywords

• Heuristic
• local search
• k-dominating set problem%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> minimum <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">k</italic>-dominating set problem