An introduction to chromatic sums
CSC '89 Proceedings of the 17th conference on ACM Annual Computer Science Conference
On chromatic sums and distributed resource allocation
Information and Computation
Minimum color sum of bipartite graphs
Journal of Algorithms
Minimal coloring and strength of graphs
Discrete Mathematics
Approximation results for the optimum cost chromatic partition problem
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Optimal Cost Chromatic Partition Problem for Trees and Interval Graphs
WG '96 Proceedings of the 22nd International Workshop on Graph-Theoretic Concepts in Computer Science
Discrete Applied Mathematics
A survey of local search methods for graph coloring
Computers and Operations Research - Anniversary focused issue of computers & operations research on tabu search
On Sum Coloring of Graphs with Parallel Genetic Algorithms
ICANNGA '07 Proceedings of the 8th international conference on Adaptive and Natural Computing Algorithms, Part I
A Metaheuristic Approach for the Vertex Coloring Problem
INFORMS Journal on Computing
Computers and Operations Research
Minimum sum set coloring of trees and line graphs of trees
Discrete Applied Mathematics
Coloring large graphs based on independent set extraction
Computers and Operations Research
A study of breakout local search for the minimum sum coloring problem
SEAL'12 Proceedings of the 9th international conference on Simulated Evolution and Learning
An adaptive multistart tabu search approach to solve the maximum clique problem
Journal of Combinatorial Optimization
A memetic algorithm for the Minimum Sum Coloring Problem
Computers and Operations Research
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Given an undirected graph G=(V,E), the minimum sum coloring problem (MSCP) is to find a legal vertex coloring of G, using colors represented by natural numbers (1,2,...) such that the total sum of the colors assigned to the vertices is minimized. In this paper, we present EXSCOL, a heuristic algorithm based on independent set extraction for this NP-hard problem. EXSCOL identifies iteratively collections of disjoint independent sets of equal size and assign to each independent set the smallest available color. For the purpose of computing large independent sets, EXSCOL employs a tabu search based heuristic. Experimental evaluations on a collection of 52 DIMACS and COLOR2 benchmark graphs show that the proposed approach achieves highly competitive results. For more than half of the graphs used in the literature, our approach improves the current best known upper bounds.