Speeding up Parallel Graph Coloring

Abstract

Abstract. This paper presents new efficient parallel algorithms for finding approximate solutions to graph coloring problems. We consider an existing shared memory parallel graph coloring algorithm and suggest several enhancements both in terms of ordering the vertices so as to minimize cache misses, and performing vertex-to-processor assignments based on graph partitioning instead of random allocation. We report experimental results that demonstrate the performance of our algorithms on an IBM Regatta supercomputer when up to 12 processors are used. Our implementations use OpenMP for parallelization and Metis for graph partitioning. The experiments show that we get up to a 70 % reduction in runtime compared to the previous algorithm.

New Graph Coloring Algorithms

“…The algorithm sequentially assigns each vertex the lowest legal color. This algorithm has the advantage of being very simple and fast and can be implemented to run in O(n) [2,3] .…”

A framework for scalable greedy coloring on distributed-memory parallel computers

“…and Woods [15] enhanced these algorithms by employing graph partitioning tools to obtain more effective assignment of vertices to processors and by using vertex orderings to minimize cache misses in a shared memory implementation.…”

“…assign v a "permissible" color c(v) 12: Send colors of boundary vertices in U i,k to other processors 13: Receive color information from other processors 14: Wait until all incoming messages are successfully received 15:…”

“…Some of these studies reported discouraging speedup results [1,17,20], while others relied on only simulations without providing actual parallel implementations [9,19]. In contrast, Gebremedhin, Manne, Pothen, and Woods reported encouraging speedup results on sharedmemory implementations of algorithms they developed in a series of inter-related works [12,13,15]. Gebremedhin, Guerin-Lassous, Gustedt, and Telle [11] extended one of these algorithms to the Coarse Grained Multicomputer model.…”

A Parallel Distance-2 Graph Coloring Algorithm for Distributed Memory Computers

“…A number of papers dealing with the design of efficient parallel distance-1 (D1) coloring algorithms have appeared [6,7,8,9]. For D2 coloring we are not aware of any work other than [10] where an algorithm for shared memory computers was presented.…”