A greedy randomized adaptive search procedure (GRASP) for minimum 2-fold connected dominating set problem

Abstract

The minimum 2-fold connected dominating set problem (M(2-fold)CDSP) is an important variant of the traditional minimum connected dominating set problem (MCDSP), with crucial applications in fields like wireless networks. Therefore, the main research purpose of this work is to design efficient algorithms for this problem in order to provide theoretical support for relevant downstream task applications. In this work, a 0-1 integer linear programming (ILP) model based on tree data structure is given firstly. Then, a greedy randomized adaptive search procedure (GRASP) framework is proposed, which consists of two procedures: construction and improvement. Based on this scheme, a two-stage initial solution construction procedure with the fusion of greedy and randomized strategies is designed, and two iterative local search procedures to improve the initial solution are proposed, resulting in our so-called GRASP and GRASP_MAR. First, in GRASP, a new vertex scoring function named Mscore, which integrates a variety of dominant cases, is designed to provide the basis of vertex movement. Second, in GRASP_MAR, two novel strategies to avoid the cyclic problem and improve performance are developed. The first strategy is random configuration checking (RCC), which is designed by improving the traditional configuration checking strategy. The main idea of RCC strategy is that using a simple parameter to control the tabu probability. The second strategy is multi-criteria search (MCS) strategy, which simultaneously considering connectivity and dominance in the movement of vertices. Experimental results show that our GRASPs, especially the GRASP_MAR, outperform all competitors, including the famous ILP solver CPLEX and three other state-of-the-art heuristic algorithms. Our proposed algorithms can efficiently and firmly deliver high-quality solutions for the M(2-fold)CDSP.