Parallel ((Greek D)D+1)-Coloring of Constant-Degree Graphs

Abstract This paper presents parallel algorithms for coloring a constant-degree graph with a maximum degree of Δ using Δ + 1 colors and for finding a maximal independent set in a constant-degree graph. Given a graph with n vertices, the algorithms run in O(lg∗n) time on an EREW PRAM with O(n) processors. The algorithms use only local communication and achieve the same complexity bounds when implemented in a distributed model of parallel computation.