Adaptive feasible and infeasible tabu search for weighted vertex coloring

2018 ◽  
Vol 466 ◽  
pp. 203-219 ◽  
Author(s):  
Wen Sun ◽  
Jin-Kao Hao ◽  
Xiangjing Lai ◽  
Qinghua Wu
Keyword(s):  
Tabu Search ◽  
Vertex Coloring ◽  
Weighted Vertex

Models and heuristic algorithms for a weighted vertex coloring problem

2008 ◽  
Vol 15 (5) ◽  
pp. 503-526 ◽  
Author(s):  
Enrico Malaguti ◽  
Michele Monaci ◽  
Paolo Toth
Keyword(s):  
Heuristic Algorithms ◽  
Vertex Coloring ◽  
Coloring Problem ◽  
Vertex Coloring Problem ◽  
Weighted Vertex

scholarly journals Exact weighted vertex coloring via branch-and-price

2012 ◽  
Vol 9 (2) ◽  
pp. 130-136 ◽  
Author(s):  
Fabio Furini ◽  
Enrico Malaguti
Keyword(s):  
Vertex Coloring ◽  
Branch And Price ◽  
Weighted Vertex

scholarly journals On new algorithmic techniques for the weighted vertex coloring problem

2020 ◽  
Vol 22 (4) ◽  
pp. 442-448
Author(s):  
Olga O. Razvenskaya
Keyword(s):  
Chromatic Number ◽  
Polynomial Time ◽  
Graph Decomposition ◽  
Vertex Coloring ◽  
Graph Reduction ◽  
Coloring Problem ◽  
Vertex Coloring Problem ◽  
Weighted Vertex ◽  
Algorithmic Techniques ◽  
Standard Techniques

The classical NP-hard weighted vertex coloring problem consists in minimizing the number of colors in colorings of vertices of a given graph so that, for each vertex, the number of its colors equals a given weight of the vertex and adjacent vertices receive distinct colors. The weighted chromatic number is the smallest number of colors in these colorings. There are several polynomial-time algorithmic techniques for designing efficient algorithms for the weighted vertex coloring problem. For example, standard techniques of this kind are the modular graph decomposition and the graph decomposition by separating cliques. This article proposes new polynomial-time methods for graph reduction in the form of removing redundant vertices and recomputing weights of the remaining vertices so that the weighted chromatic number changes in a controlled manner. We also present a method of reducing the weighted vertex coloring problem to its unweighted version and its application. This paper contributes to the algorithmic graph theory.

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