A parallel distance-2 graph coloring algorithm for distributed memory computers

Abstract

The distance-2 graph coloring problem aims at partitioning the vertex set of a graph into the fewest sets consisting of vertices pairwise at distance greater than two from each other. Application examples include numerical optimization and channel assignment. We present the first distributed-memory heuris-tic algorithm for this NP-hard problem. Parallel speedup is achieved through graph partitioning, speculative (iterative) coloring, and a BSP-like organization of computation. Experimental results show that the algorithm is scalable, and compares favorably with an alternative approach-solving the problem on a graph G by first constructing the square graph G2 and then applying a parallel distance-1 coloring algorithm on G2. © Springer-Verlag Berlin Heidelberg 2005.