A comparison of integer and constraint programming models for the deficiency problem. (April 2016) - Altinakar, Sivan; Caporossi, Gilles; Hertz, Alain
Abstract: An edge-coloring of a graph G = ( V, E ) is a function c that assigns an integer c ( e ) (called color) in 0, 1, 2, … to every edge e ∈ E so that adjacent edges are assigned different colors. An edge-coloring is compact if the colors of the edges incident to every vertex form a set of consecutive integers. The deficiency problem is to determine the minimum number of pendant edges that must be added to a graph such that the resulting graph admits a compact edge-coloring. We propose and analyze three integer programming models and one constraint programming model for the deficiency problem. Abstract : Highlights: We describe integer and constraint programming models for the deficiency problem. We obtain bounds on the number of colors in an edge-coloring with minimum deficiency. We clearly show that symmetry breaking constraints decrease the computing time.