scholarly journals Solving Set Cover and Dominating Set via Maximum Satisfiability

2020 ◽  
Vol 34 (02) ◽  
pp. 1569-1576 ◽  
Author(s):  
Zhendong Lei ◽  
Shaowei Cai
Keyword(s):  
Local Search ◽  
Large Scale ◽  
Dominating Set ◽  
Scoring Function ◽  
Initial Solution ◽  
Set Covering ◽  
Set Cover ◽  
Covering Problem ◽  
Greedy Heuristic ◽  
Maximum Satisfiability

The Set Covering Problem (SCP) and Dominating Set Problem (DSP) are NP-hard and have many real world applications. SCP and DSP can be encoded into Maximum Satisfiability (MaxSAT) naturally and the resulting instances share a special structure. In this paper, we develop an efficient local search solver for MaxSAT instances of this kind. Our algorithm contains three phrase: construction, local search and recovery. In construction phrase, we simplify the instance by three reduction rules and construct an initial solution by a greedy heuristic. The initial solution is improved during the local search phrase, which exploits the feature of such instances in the scoring function and the variable selection heuristic. Finally, the corresponding solution of original instance is recovered in the recovery phrase. Experiment results on a broad range of large scale instances of SCP and DSP show that our algorithm significantly outperforms state of the art solvers for SCP, DSP and MaxSAT.

scholarly journals Local Search for Minimum Weight Dominating Set with Two-Level Configuration Checking and Frequency Based Scoring Function (Extended Abstract)

2017 ◽  
Author(s):  
Yiyuan Wang ◽  
Shaowei Cai ◽  
Minghao Yin
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Dominating Set ◽  
Minimum Weight ◽  
Scoring Function ◽  
Solution Quality ◽  
Configuration Checking ◽  
New Variant ◽  
New Ideas ◽  
Better Than

The Minimum Weight Dominating Set (MWDS) problem is an important generalization of the Minimum Dominating Set (MDS) problem with extensive applications. This paper proposes a new local search algorithm for the MWDS problem, which is based on two new ideas. The first idea is a heuristic called two-level configuration checking (CC2), which is a new variant of a recent powerful configuration checking strategy (CC) for effectively avoiding the recent search paths. The second idea is a novel scoring function based on the frequency of being uncovered of vertices. Our algorithm is called CC2FS, according to the names of the two ideas. The experimental results show that, CC2FS performs much better than some state-of-the-art algorithms in terms of solution quality on a broad range of MWDS benchmarks.

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

2021 ◽  
Vol 71 ◽  
pp. 89-119
Author(s):  
Xindi Zhang ◽  
Bohan Li ◽  
Shaowei Cai ◽  
Yiyuan Wang
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Dominating Set ◽  
Practical Importance ◽  
Scoring Function ◽  
Connected Dominating Set ◽  
Minimum Connected Dominating Set ◽  
Important Extension ◽  
Connectivity Maintenance ◽  
Dynamic Connectivity

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.

scholarly journals A New Formulation of the Set Covering Problem for Metaheuristic Approaches

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Nehme Bilal ◽  
Philippe Galinier ◽  
Francois Guibault
Keyword(s):  
Optimization Problem ◽  
Set Covering ◽  
Covering Problem ◽  
Greedy Heuristic ◽  
Test Problems ◽  
Set Covering Problem ◽  
Computational Results ◽  
Unconstrained Optimization Problem ◽  
New Formulation ◽  
Neighbourhood Structure

Two difficulties arise when solving the set covering problem (SCP) with metaheuristic approaches: solution infeasibility and set redundancy. In this paper, we first present a review and analysis of the heuristic approaches that have been used in the literature to address these difficulties. We then present a new formulation that can be used to solve the SCP as an unconstrained optimization problem and that eliminates the need to address the infeasibility and set redundancy issues. We show that all local optimums with respect to the new formulation and a 1-flip neighbourhood structure are feasible and free of redundant sets. In addition, we adapt an existing greedy heuristic for the SCP to the new formulation and compare the adapted heuristic to the original heuristic using 88 known test problems for the SCP. Computational results show that the adapted heuristic finds better results than the original heuristic on most of the test problems in shorter computation times.

scholarly journals Local Search for Minimum Weight Dominating Set with Two-Level Configuration Checking and Frequency Based Scoring Function

2017 ◽  
Vol 58 ◽  
pp. 267-295 ◽  
Author(s):  
Yiyuan Wang ◽  
Shaowei Cai ◽  
Minghao Yin
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Dominating Set ◽  
Minimum Weight ◽  
Scoring Function ◽  
Solution Quality ◽  
Configuration Checking ◽  
New Variant ◽  
New Ideas ◽  
Better Than

The Minimum Weight Dominating Set (MWDS) problem is an important generalization of the Minimum Dominating Set (MDS) problem with extensive applications. This paper proposes a new local search algorithm for the MWDS problem, which is based on two new ideas. The first idea is a heuristic called two-level configuration checking (CC2), which is a new variant of a recent powerful configuration checking strategy (CC) for effectively avoiding the recent search paths. The second idea is a novel scoring function based on the frequency of being uncovered of vertices. Our algorithm is called CC2FS, according to the names of the two ideas. The experimental results show that, CC2FS performs much better than some state-of-the-art algorithms in terms of solution quality on a broad range of MWDS benchmarks.

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