A reduction based method for coloring very large graphs
Jinkun Lin,Shaowei Cai,Chuan Luo,Kaile Su +3 more
- 01 Aug 2017
- pp 517-523
TL;DR: A reduction rule is proposed for GCP, which is based on a novel concept called degree bounded independent set, and a novel method called FastColor is developed, which also exploits fast clique and coloring heuristics, and proves an optimal solution when the upper bound meets the lower bound.
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Abstract: The graph coloring problem (GCP) is one of the most studied NP hard problems and has numerous applications. Despite the practical importance of GCP, there are limited works in solving GCP for very large graphs. This paper explores techniques for solving GCP on very large real world graphs.We first propose a reduction rule for GCP, which is based on a novel concept called degree bounded independent set.The rule is iteratively executed by interleaving between lower bound computation and graph reduction. Based on this rule, we develop a novel method called FastColor, which also exploits fast clique and coloring heuristics. We carry out experiments to compare our method FastColor with two best algorithms for coloring large graphs we could find. Experiments on a broad range of real world large graphs show the superiority of our method. Additionally, our method maintains both upper bound and lower bound on the optimal solution, and thus it proves an optimal solution when the upper bound meets the lower bound. In our experiments, it proves the optimal solution for 97 out of 142 instances.
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Citations
A Fast Local Search Algorithm for Minimum Weight Dominating Set Problem on Massive Graphs
Yiyuan Wang,Yiyuan Wang,Shaowei Cai,Jiejiang Chen,Jiejiang Chen,Minghao Yin,Minghao Yin +6 more
- 01 Jul 2018
TL;DR: A fast local search algorithm for the minimum weight dominating set problem, which aims to obtain a good solution on massive graphs within a short time, and proposes the three-valued two-level configuration checking strategy to improve local search, which is interestingly a variant of configuration checking with two levels and multiple values.
SCCWalk: An efficient local search algorithm and its improvements for maximum weight clique problem
TL;DR: Experiments show that the proposed algorithms perform better on classical benchmarks, and obtain the best solutions for most massive graphs, compared to state-of-the-art heuristic algorithms and exact algorithm.
54
Partition Independent Set and Reduction-Based Approach for Partition Coloring Problem.
TL;DR: This article proposes a key concept called a partition independent set (PIS) and designs an efficient algorithm called FastPIS to find a maximum PIS, and develops an efficient method called HotPGC for solving PCP, which achieves highly competitive performance, compared with the state-of-the-art algorithms.
33
Faster exact solution of sparse MaxCut and QUBO problems
TL;DR: In this paper , a branch-and-cut solver for sparse maximum-cut and quadratic unconstrained binary optimization instances is presented. But the main focus lies on sparse problem instances, although also dense ones can be solved.
Reduction and Local Search for Weighted Graph Coloring Problem
Yiyuan Wang,Shaowei Cai,Shiwei Pan,Ximing Li,Monghao Yin +4 more
- 03 Apr 2020
TL;DR: Techniques for solving WGCP are explored, 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, resulting in the algorithm RedLS (Reduction plus Local Search).
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