High-Performance Parallel Graph Coloring with Strong Guarantees on Work, Depth and Quality

Authors: Maciej Besta and Armon Carigiet (ETH Zurich); Kacper Janda (AGH University of Science and Technology); and Zur Vonarburg-Shmaria, Lukas Gianinazzi, and Torsten Hoefler (ETH Zurich)

Abstract: We develop the first parallel graph coloring heuristic with strong theoretical guarantees on work and depth and coloring quality. The key idea is to design a relaxation of the vertex degeneracy order, a well-known graph theory concept, and to color vertices in the order dictated by this relaxation. This introduces a tunable amount of parallelism into the degeneracy ordering that is otherwise hard to parallelize. This simple idea enables significant benefits in several key aspects of graph coloring. For example, one of our algorithms ensures polylogarithmic depth and a bound on the number of used colors that is superior to all other parallelizable schemes, while maintaining work efficiency. In addition to provable guarantees, the developed algorithms have competitive runtimes for several real-world graphs, while almost always providing superior coloring quality. Our degeneracy ordering relaxation is of separate interest for algorithms outside the context of coloring.




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