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.

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 A Fast Local Search Algorithm for Minimum Weight Dominating Set Problem on Massive Graphs

2018 ◽  
Author(s):  
Yiyuan Wang ◽  
Shaowei Cai ◽  
Jiejiang Chen ◽  
Minghao Yin
Keyword(s):  
Local Search ◽  
Real World ◽  
Search Algorithm ◽  
Dominating Set ◽  
Minimum Weight ◽  
Local Search Algorithm ◽  
Massive Graphs ◽  
Configuration Checking ◽  
Dominating Set Problem ◽  
Short Time

The minimum weight dominating set (MWDS) problem is NP-hard and also important in many applications. Recent heuristic MWDS algorithms can hardly solve massive real world graphs effectively. In this paper, we design a fast local search algorithm called FastMWDS for the MWDS problem, which aims to obtain a good solution on massive graphs within a short time. In this novel local search framework, we propose two ideas to make it effective. Firstly, we design a new fast construction procedure with four reduction rules to cut down the size of massive graphs. Secondly, we propose the three-valued two-level configuration checking strategy to improve local search, which is interestingly a variant of configuration checking (CC) with two levels and multiple values. Experiment results on a broad range of massive real world graphs show that FastMWDS finds much better solutions than state of the art MWDS algorithms.

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

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1173 ◽  
Author(s):  
Ruizhi Li ◽  
Shuli Hu ◽  
Huan Liu ◽  
Ruiting Li ◽  
Dantong Ouyang ◽  
...  
Keyword(s):  
Local Search ◽  
Ad Hoc ◽  
Search Algorithm ◽  
Dominating Set ◽  
Connected Dominating Set ◽  
Local Optimum ◽  
Local Search Algorithm ◽  
Solution Quality ◽  
Minimum Connected Dominating Set ◽  
Hoc Networks

The minimum connected dominating set (MCDS) problem is a very significant NP-hard combinatorial optimization problem, and it has been used in many fields such as wireless sensor networks and ad hoc networks. In this paper, we propose a novel multi-start local search algorithm (MSLS) to tackle the minimum connected dominating set problem. Firstly, we present the fitness mechanism to design the vertex score mechanism so that our algorithm can jump out of the local optimum. Secondly, we use the configuration checking (CC) mechanism to avoid the cycling problem. Then, we propose the vertex flipping mechanism to change the vertex state by combing the CC mechanism with the vertex score mechanism. Finally, we propose a multi-start local search framework based on these mechanisms. We compare the algorithm MSLS with other compared algorithms on extensive instances. The results of experiment show that MSLS is superior to other algorithms in solution quality and time efficiency on most instances.

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 Reduction and Local Search for Weighted Graph Coloring Problem

2020 ◽  
Vol 34 (03) ◽  
pp. 2433-2441 ◽  
Author(s):  
Yiyuan Wang ◽  
Shaowei Cai ◽  
Shiwei Pan ◽  
Ximing Li ◽  
Monghao Yin
Keyword(s):  
Local Search ◽  
Graph Coloring ◽  
Search Algorithm ◽  
Weighted Graph ◽  
Coloring Problem ◽  
Massive Graphs ◽  
Configuration Checking ◽  
New Variant ◽  
Graph Coloring Problem ◽  
Important Extension

The weighted graph coloring problem (WGCP) is an important extension of the graph coloring problem (GCP) with wide applications. Compared to GCP, where numerous methods have been developed and even massive graphs with millions of vertices can be solved well, fewer works have been done for WGCP, and no solution is available for solving WGCP for massive graphs. This paper explores techniques for solving WGCP, including a lower bound and a reduction rule based on clique sampling, and a local search algorithm based on two selection rules and a new variant of configuration checking. This results in our algorithm RedLS (Reduction plus Local Search). Experiments are conducted to compare RedLS with the state-of-the-art algorithms on massive graphs as well as conventional benchmarks studied in previous works. RedLS exhibits very good performance and robustness. It significantly outperforms previous algorithms on all benchmarks.

A novel local search algorithm for the minimum capacitated dominating set

2018 ◽  
Vol 69 (6) ◽  
pp. 849-863 ◽  
Author(s):  
Ruizhi Li ◽  
Shuli Hu ◽  
Peng Zhao ◽  
Yupeng Zhou ◽  
Minghao Yin
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Dominating Set ◽  
Local Search Algorithm

scholarly journals Two-goal Local Search and Inference Rules for Minimum Dominating Set

2020 ◽  
Author(s):  
Shaowei Cai ◽  
Wenying Hou ◽  
Yiyuan Wang ◽  
Chuan Luo ◽  
Qingwei Lin
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Dominating Set ◽  
Inference Rules ◽  
Local Search Algorithm ◽  
Minimum Dominating Set ◽  
Massive Graphs ◽  
Construction Procedure ◽  
Almost All ◽  
Main Ideas

Minimum dominating set (MinDS) is a canonical NP-hard combinatorial optimization problem with applications. For large and hard instances one must resort to heuristic approaches to obtain good solutions within reasonable time. This paper develops an efficient local search algorithm for MinDS, which has two main ideas. The first one is a novel local search framework, while the second is a construction procedure with inference rules. Our algorithm named FastDS is evaluated on 4 standard benchmarks and 3 massive graphs benchmarks. FastDS obtains the best performance for almost all benchmarks, and obtains better solutions than state-of-the-art algorithms on massive graphs.

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 with Dynamic-Threshold Configuration Checking and Incremental Neighborhood Updating for Maximum k-plex Problem

2020 ◽  
Vol 34 (03) ◽  
pp. 2343-2350 ◽  
Author(s):  
Peilin Chen ◽  
Hai Wan ◽  
Shaowei Cai ◽  
Jia Li ◽  
Haicheng Chen
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Promising Result ◽  
Dynamic Threshold ◽  
Local Search Algorithm ◽  
Local Search Algorithms ◽  
Worst Case ◽  
Massive Graphs ◽  
Configuration Checking ◽  
Novel Strategy

The Maximum k-plex Problem is an important combinatorial optimization problem with increasingly wide applications. In this paper, we propose a novel strategy, named Dynamic-threshold Configuration Checking (DCC), to reduce the cycling problem of local search. Due to the complicated neighborhood relations, all the previous local search algorithms for this problem spend a large amount of time in identifying feasible neighbors in each step. To further improve the performance on dense and challenging instances, we propose Double-attributes Incremental Neighborhood Updating (DINU) scheme which reduces the worst-case time complexity per iteration from O(|V|⋅ΔG) to O(k · Δ‾G). Based on DCC strategy and DINU scheme, we develop a local search algorithm named DCCplex. According to the experiment result, DCCplex shows promising result on DIMACS and BHOSLIB benchmark as well as real-world massive graphs. Especially, DCCplex updates the lower bound of the maximum k-plex for most dense and challenging instances.

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