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.

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.

A Modified Binary Crow Search Algorithm for Solving the Graph Coloring Problem

2020 ◽  
Vol 11 (2) ◽  
pp. 28-46 ◽  
Author(s):  
Yassine Meraihi ◽  
Mohammed Mahseur ◽  
Dalila Acheli
Keyword(s):  
Graph Coloring ◽  
Optimization Problem ◽  
Heuristic Algorithms ◽  
Search Algorithm ◽  
Distribution Method ◽  
Local Optima ◽  
Coloring Problem ◽  
Graph Coloring Problem ◽  
Np Hard Problem ◽  
The Right

The graph coloring problem (GCP) is a well-known classical combinatorial optimization problem in graph theory. It is known to be an NP-Hard problem, so many heuristic algorithms have been employed to solve this problem. This article proposes a modified binary crow search algorithm (MBCSA) to solve the graph coloring problem. First, the binary crow search algorithm is obtained from the original crow search algorithm using the V-shaped transfer function and the discretization method. Second, we use chaotic maps to choose the right values of the flight length (FL) and the awareness probability (AP). Third, we adopt the Gaussian distribution method to replace the random variables used for updating the position of the crows. The aim of these contributions is to avoid the premature convergence to local optima and ensure the diversity of the solutions. To evaluate the performance of our algorithm, we use the well-known DIMACS benchmark graph coloring instances. The simulation results reveal the efficiency of our proposed algorithm in comparison with other existing algorithms in the literature.

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 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 NuCDS: An Efficient Local Search Algorithm for Minimum Connected Dominating Set

2020 ◽  
Author(s):  
Bohan Li ◽  
Xindi Zhang ◽  
Shaowei Cai ◽  
Jinkun Lin ◽  
Yiyuan Wang ◽  
...  
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Dominating Set ◽  
Practical Importance ◽  
Connected Dominating Set ◽  
Local Search Algorithm ◽  
Massive Graphs ◽  
Minimum Connected Dominating Set ◽  
Important Extension ◽  
Connectivity Maintenance

The minimum connected dominating set (MCDS) problem is an important extension of the minimum dominating set problem, with wide applications, especially in wireless networks. Despite its practical importance, there are few works on solving MCDS for massive graphs, mainly due to the complexity of maintaining connectivity. In this paper, we propose two novel ideas, and develop a new local search algorithm for MCDS called NuCDS. First, a hybrid dynamic connectivity maintenance method is designed to switch alternately between a novel fast connectivity maintenance method based on spanning tree and its previous counterpart. Second, we define a new vertex property called \emph{safety} to make the algorithm more considerate when selecting vertices. Experiments show that NuCDS significantly outperforms the state-of-the-art MCDS algorithms on both massive graphs and classic benchmarks.

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