Multi-Start Local Search Algorithm for the Minimum Connected Dominating Set Problems

Li, Ruizhi; Hu, Shuli; Liu, Huan; Li, Ruiting; Ouyang, Dantong; Yin, Minghao

doi:10.3390/math7121173

Cited by 18 publications

(11 citation statements)

References 44 publications

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“…The first version, used in ACO-RVNS (Bouamama et al, 2019) and in MCDS/TS (Morgan & Grout, 2007), works as follows: during each iteration, the algorithm starts from an empty candidate solution D, and iteratively adds a vertex from N (D) to D until D becomes a feasible solution. The second version, used in GRASP (Li et al, 2017) and MSLS (Li et al, 2019), works as follows: the algorithm allows removing articulation vertices of D, so D may become disconnected. Thus, before vertex u is selected to be added, DFS is used to calculate the number of con-nected subgraphs of D that v ∈ N (u) belongs to, and the vertex with the largest number is preferred.…”

Section: Previous Connectivity Maintenance Methodsmentioning

confidence: 99%

“…Two meta-heuristics based on genetic algorithms and simulated annealing were designed to solve MCDS problem (Hedar et al, 2019). Li et al presented a multi-start local search algorithm called MSLS based on three mechanisms including a vertex score, configuration checking, and vertex flipping (Li et al, 2019). Finally, a meta-heuristic algorithm called ACO-RVNS (Bouamama et al, 2019) was proposed, based on ant colony optimization and reduced variable neighborhood search.…”

Section: Previous Workmentioning

confidence: 99%

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

Zhang¹,

Li²,

Wang³

2021

jair

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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.

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Section: Previous Connectivity Maintenance Methodsmentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

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

Zhang¹,

Li²,

Wang³

2021

jair

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“…In the literature, there are many variants of the MDS problem. Examples include the minimum connected dominating set problem [34], the minimum total dominating set problem [35] and the minimum vertex weight dominating set problem [36]. The currently best metaheuristic approach for solving the MDS problem is a two-goal local search with inference rules from [37].…”

Section: Minimum Dominating Setmentioning

confidence: 99%

Adding Negative Learning to Ant Colony Optimization: A Comprehensive Study

Nurcahyadi

Blum

2021

Mathematics

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Ant colony optimization is a metaheuristic that is mainly used for solving hard combinatorial optimization problems. The distinctive feature of ant colony optimization is a learning mechanism that is based on learning from positive examples. This is also the case in other learning-based metaheuristics such as evolutionary algorithms and particle swarm optimization. Examples from nature, however, indicate that negative learning—in addition to positive learning—can beneficially be used for certain purposes. Several research papers have explored this topic over the last decades in the context of ant colony optimization, mostly with limited success. In this work we present and study an alternative mechanism making use of mathematical programming for the incorporation of negative learning in ant colony optimization. Moreover, we compare our proposal to some well-known existing negative learning approaches from the related literature. Our study considers two classical combinatorial optimization problems: the minimum dominating set problem and the multi dimensional knapsack problem. In both cases we are able to show that our approach significantly improves over standard ant colony optimization and over the competing negative learning mechanisms from the literature.

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“…To better understand this relationship, Definition 1 describes what a dominating set is and Definition 2 describes what a minimum dominating set is. Then, Expressions (16) to (19) show the integer programming formulation for the uncapacitated vertex k-center as a minimum dominating set problem [11,[36][37][38].…”

Section: A New Formulation Based On the Minimum Capacitated Dominatinmentioning

confidence: 99%

Solving the Capacitated Vertex K-Center Problem through the Minimum Capacitated Dominating Set Problem

et al. 2020

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The capacitated vertex k-center problem receives as input a complete weighted graph and a set of capacity constraints. Its goal is to find a set of k centers and an assignment of vertices that does not violate the capacity constraints. Furthermore, the distance from the farthest vertex to its assigned center has to be minimized. The capacitated vertex k-center problem models real situations where a maximum number of clients must be assigned to centers and the travel time or distance from the clients to their assigned center has to be minimized. These centers might be hospitals, schools, police stations, among many others. The goal of this paper is to explicitly state how the capacitated vertex k-center problem and the minimum capacitated dominating set problem are related. We present an exact algorithm that consists of solving a series of integer programming formulations equivalent to the minimum capacitated dominating set problem over the bottleneck input graph. Lastly, we present an empirical evaluation of the proposed algorithm using off-the-shelf optimization software.

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Multi-Start Local Search Algorithm for the Minimum Connected Dominating Set Problems

Cited by 18 publications

References 44 publications

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

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

Adding Negative Learning to Ant Colony Optimization: A Comprehensive Study

Solving the Capacitated Vertex K-Center Problem through the Minimum Capacitated Dominating Set Problem

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