Sum Coloring : New upper bounds for the chromatic strength

The Minimum Sum Coloring Problem (MSCP ) is derived from the Graph Coloring Problem (GCP ) by associating a weight to each color. The aim ofMSCP is to find a coloring solution of a graph such that the sum of color weights is minimum.MSCP has important applications in fields such as scheduling and VLSI design. We propose in this paper new upper bounds of the chromatic strength, i.e. the minimum number of colors in an optimal solution of MSCP , based on an abstraction of all possible colorings of a graph called motif. Experimental results on standard benchmarks show that our new bounds are significantly tighter than the previous bounds in general, allowing to reduce substantially the search space when solving MSCP .