A fast local search algorithm for minimum sum coloring problem on massive graphs

The minimum sum coloring problem (MSCP) is an important extension of the graph coloring problem with wide real-world applications. Compared to the classic graph coloring problem, where lots of methods have been developed and even massive graphs with millions of vertices can be solved well, few works have been done for the MSCP, and no specialized MSCP algorithms are available for solving massive graphs. This paper explores how to solve MSCP on massive graphs, and then proposes a fast local search algorithm for the MSCP based on three main ideas including a coarse-grained reduction method, two kinds of scoring functions and selection rules as well as a novel local search framework. Experiments are conducted to compare our algorithm with several state-of-the-art algorithms on massive graphs. The proposed algorithm outperforms previous algorithms in almost all the massive graphs and also improves the best-known solutions for some conventional instances, which demonstrates the performance and robustness of the proposed algorithm.