Graph Coloring using CUDA

ion of computation For a graph G = (V,E), we denote the number of vertices |V| by n, the number of edges|E| by m, and the degree of a vertex vi by deg(vi). The maximum, minimum, and average degree in a graph are denoted by (delta), (sigma), and (sigma -) respectively. The minimum number of colors required to color a graph is referred to as the Chromatic number. There exists several fast sequential coloring heuristics. They are based on the same general greedy framework: a vertex is selected according to some predefined criterion and then colored with the smallest valid color. The selection and coloring continues until all the vertices in the graph are colored. For our project we are more interested in parallel version of these algorithms. Quite a few have been suggested in [1] but they fail to get any speedup as the number of processors increase. However, in [3] and [6] they do get speed up as the number of processors increase and so we are going to focus on that. The algorithm is shown below: Algorithm details GM-Algorithm from [6] Phase 0 : Partition Randomly partition V into p equal blocks V1 ..... Vp. Each processor Pi is responsible for coloring the vertices in block Vi. Phase 1 : Pseudo-color for i = 1 to p do in parallel for each v 2 Vi do assign a legal color to v, paying attention to already colored vertices (both on and off processor).