Efficient Local Search based on Dynamic Connectivity Maintenance for Minimum Connected Dominating Set

Abstract

The minimum connected dominating set (MCDS) problem is an important extension of the minimum dominating set problem, with wide applications, especially in wireless networks. Most previous works focused on solving MCDS problem in graphs with relatively small size, mainly due to the complexity of maintaining connectivity. This paper explores techniques for solving MCDS problem in massive real-world graphs with wide practical importance. Firstly, we propose a local greedy construction method with reasoning rule called 1hopReason. Secondly and most importantly, a hybrid dynamic connectivity maintenance method (HDC+) is designed to switch alternately between a novel fast connectivity maintenance method based on spanning tree and its previous counterpart. Thirdly, we adopt a two-level vertex selection heuristic with a newly proposed scoring function called chronosafety to make the algorithm more considerate when selecting vertices. We design a new local search algorithm called FastCDS based on the three ideas. Experiments show that FastCDS significantly outperforms five state-of-the-art MCDS algorithms on both massive graphs and classic benchmarks.

Improving Simulated Annealing for Clique Partitioning Problems

“…Heuristics, especially local search methods that move from solution to solution in the space of candidate solutions by applying local changes, play an important role in solving NP-hard problems. For the last decades, various heuristic algorithms have been proposed to find high-quality solutions for large-scale instances in an acceptable time and computer memory (Wang et al, 2017;Lu et al, 2020;Zhang et al, 2021;Lu et al, 2021;Bilandi et al, 2021). Among heuristic algorithms, tabu search (Glover, 1989(Glover, , 1990 and simulated annealing (Skiscim & Golden, 1983;Kirkpatrick et al, 1983), which solved many graph problems successfully (Palubeckis et al, 2014;Bilandi et al, 2021;Lu et al, 2019), showed their efficiency in solving many benchmark instances of the CPP.…”

“…For more detailed relationships of the configuration checking strategy and the tabu method, we refer to (Cai et al, 2011). The configuration checking strategy has proven effective to solve problems in graph theory and SAT problems Luo et al, 2013Luo et al, , 2015Wang et al, 2017;Zhang et al, 2021). The main idea of the configuration checking strategy is to prevent a stochastic local search algorithm from revisiting the same scenario by checking whether the states or neighbors' states of a vertex have changed or not.…”

Secure multicasting in wireless sensor networks using identity based cryptography

“…Zhang et al 28 explored techniques for solving minimum connected dominating set problems in massive real‐world graphs with wide practical importance. The authors implemented the local greedy construction method with a reasoning rule called 1hopReason.The advantages of this proposed method are a hybrid dynamic connectivity maintenance method and a novel fast connectivity maintenance method based on a spanning tree.…”