Recent Advances in Graph Vertex Coloring

Galinier, P.; Hamiez, Jean-Philippe; Hao, Jin‐Kao; Porumbel, Daniel Cosmin

doi:10.1007/978-3-642-30504-7_20

Cited by 43 publications

(39 citation statements)

References 69 publications

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“…Notice that GCP can be approximated by solving a series of k-GCP (with decreasing k) as follows [16]. For a given G and a given k, we use our RLS approach to solve k-GCP by seeking a legal k-coloring.…”

Section: Graph Coloring and Local Search Coloring Algorithmmentioning

confidence: 99%

Reinforcement learning based local search for grouping problems: A case study on graph coloring

Zhou

Hao

Duval

2016

Expert Systems with Applications

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Grouping problems aim to partition a set of items into multiple mutually disjoint subsets according to some specific criterion and constraints. Grouping problems cover a large class of important combinatorial optimization problems that are generally computationally difficult. In this paper, we propose a general solution approach for grouping problems, i.e., reinforcement learning based local search (RLS), which combines reinforcement learning techniques with descent-based local search. The viability of the proposed approach is verified on a well-known representative grouping problem (graph coloring) where a very simple descent-based coloring algorithm is applied. Experimental studies on popular DIMACS and COLOR02 benchmark graphs indicate that RLS achieves competitive performances compared to a number of well-known coloring algorithms.

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Section: Graph Coloring and Local Search Coloring Algorithmmentioning

confidence: 99%

Reinforcement learning based local search for grouping problems: A case study on graph coloring

Zhou

Hao

Duval

2016

Expert Systems with Applications

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“…As a basis for determining the equitable chromatic number of a graph by finding the smallest number k of colors such that an equitable k-coloring exists, we employ the fact that, like the GCP [14,16,17], the ECP can be approximated by solving a series of k-ECP problems with decreasing k values, where a k-ECP problem aims at searching for a legal equitable k-coloring for a given fixed k value. This approach is called k-fixed penalty approach in the context of the GCP [14,16] and used in TabuEqCol [24] for the ECP.…”

Section: Solution Approach and General Proceduresmentioning

confidence: 99%

“…This approach is called k-fixed penalty approach in the context of the GCP [14,16] and used in TabuEqCol [24] for the ECP. Our BITS algorithm, however, adopts this general solution approach with a notable difference.…”

Section: Solution Approach and General Proceduresmentioning

confidence: 99%

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Backtracking based iterated tabu search for equitable coloring

Lai

Hao

Glover

2015

Engineering Applications of Artificial Intelligence

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An equitable k-coloring of an undirected graph G = (V, E) is a partition of its vertices into k disjoint independent sets, such that the cardinalities of any two independent sets differ by at most one. As a variant of the graph coloring problem (GCP), the equitable coloring problem (ECP) concerns finding a minimum k for which an equitable k-coloring exists. In this work, we propose a backtracking based iterated tabu search (BITS) algorithm for solving the ECP approximately. BITS uses a backtracking scheme to define different k-ECP instances, an iterated tabu search approach to solve each particular k-ECP instance for a fixed k, and a binary search approach to find a suitable initial value of k. We assess the algorithm's performance on a set of commonly used benchmarks. Computational results show that BITS is very competitive in terms of solution quality and computing efficiency compared to the state-of-the-art algorithm in the literature. Specifically, BITS obtains new upper bounds for 21 benchmark instances, while matching the previous best upper bound for the remaining instances. Finally, to better understand the proposed algorithm, we study how its key ingredients impact its performance.

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“…• Other variants with some additional constraints More applications, as well as other discussions considering graph coloring and its generalizations is out of the paper's scope and can be found for example in [6,11,12].…”

Section: Introductionmentioning

confidence: 99%

Variable neighborhood search for solving bandwidth coloring problem

Matić¹,

Kratica

Filipović

2017

COMSIS J

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This paper presents a variable neighborhood search (VNS) algorithm for solving bandwidth coloring problem (BCP) and bandwidth multicoloring problem (BMCP). BCP and BMCP are generalizations of the well known vertex coloring problem and they are of a great interest from both theoretical and practical points of view. Presented VNS combines a shaking procedure which perturbs the colors for an increasing number of vertices and a specific variable neighborhood descent (VND) procedure, based on the specially designed arrangement of the vertices which are the subject of re-coloring. By this approach, local search is split in a series of disjoint procedures, enabling better choice of the vertices which are addressed to re-color. The experiments show that proposed method is highly competitive with the state-of-the-art algorithms and improves 2 out of 33 previous best known solutions for BMCP.

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Recent Advances in Graph Vertex Coloring

Cited by 43 publications

References 69 publications

Reinforcement learning based local search for grouping problems: A case study on graph coloring

Reinforcement learning based local search for grouping problems: A case study on graph coloring

Backtracking based iterated tabu search for equitable coloring

Variable neighborhood search for solving bandwidth coloring problem

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