On Distributed Graph Coloring with Iterative Recoloring

Abstract: Identifying the sets of operations that can be executed simultaneously is an important problem appearing in many parallel applications. By modeling the operations and their interactions as a graph, one can identify the independent operations by solving a graph coloring problem. Many efficient sequential algorithms are known for this NP-Complete problem, but they are typically unsuitable when the operations and their interactions are distributed in the memory of large parallel computers. On top of an existing distributed-memory graph coloring algorithm, we investigate two compatible techniques in this paper for fast and scalable distributed-memory graph coloring. First, we introduce an improvement for the distributed post-processing operation, called recoloring, which drastically improves the number of colors. We propose a novel and efficient communication scheme for recoloring which enables it to scale gracefully. Recoloring must be seeded with an existing coloring of the graph. Our second contribution is to introduce a randomized color selection strategy for initial coloring which quickly produces solutions of modest quality. We extensively evaluate the impact of our new techniques on existing distributed algorithms and show the time-quality tradeoffs. We show that combining an initial randomized coloring with multiple recoloring iterations yields better quality solutions with the smaller runtime at large scale.