Efficient coloring of a large spectrum of graphs

Abstract

We have developed a new algorithm and software for graph coloring by systematically combining several algorithm and software development ideas that had crucial impact an the algorithm's performance. The algorithm explores the divide-and-conquer paradigm, global search for constrained independent sets using a computationally inexpensive objective function, assignment of most-constrained vertices to least-constraining colors, reuse and locality exploration of intermediate solutions, search time management, post-processing lottery-scheduling iterative improvement, and statistical parameter determination and validation. The algorithm was tested on a set of real-life examples. We found that hard-to-color real-life examples are common especially in domains where problem modeling results in denser graphs. Systematic experimentations demonstrated that for numerous instances the algorithm outperformed all other implementations reported in literature in solution quality and run-time.