Safe Lower Bounds for Graph Coloring
نویسندگان
چکیده
The best known method for determining lower bounds on the vertex coloring number of a graph is the linear-programming column-generation technique first employed by Mehrotra and Trick in 1996. We present an implementation of the method that provides numerically safe results, independent of the floating-point accuracy of linearprogramming software. Our work includes an improved branch-and-bound algorithm for maximum-weight stable sets and a parallel branch-and-price framework for graph coloring. Computational results are presented on a collection standard test instances, including the unsolved challenge problems created by David S. Johnson in 1989. ∗Research supported by DAAD †Research supported by NSF Grant CMMI-0726370 and ONR Grant N00014-08-1-1104.
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تاریخ انتشار 2011