Maximum-weight stable sets and safe lower bounds for graph coloring
نویسندگان
چکیده
The best method known for determining lower bounds on the vertex coloring number of a graph is the linear-programming column-generation technique, where variables correspond to stable sets, 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 linear-programming software. Our work includes an improved branch-andbound algorithm for maximum-weight stable sets and a parallel branch-andprice framework for graph coloring. Computational results are presented on a collection of standard test instances, including the unsolved challenge problems created by David S. Johnson in 1989.
منابع مشابه
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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 a...
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ورودعنوان ژورنال:
- Math. Program. Comput.
دوره 4 شماره
صفحات -
تاریخ انتشار 2012