Scalable parallel graph coloring algorithms

Abstract

SUMMARYFinding a good graph coloring quickly is often a crucial phase in the development of efficient, parallel algorithms for many scientific and engineering applications. In this paper we consider the problem of solving the graph coloring problem itself in parallel. We present a simple and fast parallel graph coloring heuristic that is well suited for shared memory programming and yields an almost linear speedup on the PRAM model. We also present a second heuristic that improves on the number of colors used. The heuristics have been implemented using OpenMP. Experiments conducted on an SGI Cray Origin 2000 supercomputer using very large graphs from finite element methods and eigenvalue computations validate the theoretical run-time analysis.

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

“…Gebremedhin and Manne [12] developed a simple, shared-memory parallel coloring algorithm that gave fairly good speedup in practice. In their algorithm, the vertex set is equi-partitioned among the available processors and each processor colors its assigned set of vertices in a sequential fashion, at each step assigning a vertex the smallest color not used by any of its on-or off-processor neighbors; the assigned color information is immediately made available to other processors by writing to shared memory.…”

“…Gebremedhin, Manne, and Pothen [13] extended the algorithms in [12] to the distance-2 and star coloring problems, models that occur in the computation of Jacobian and…”

“…In a different direction, Gebremedhin, Guérin-Lassous, Gustedt, and Telle [11] extended the algorithm in [12] [32,3]. Besides paying attention to cost associated with non-local data access, the randomized as well as deterministic CGM-coloring algorithms proposed in [11].…”

“…Here, only the graph induced by boundary vertices involved in conflicts is constructed on one dedicated processor and then colored sequentially by the same processor. Note that the algorithm of Gebremedhin and Manne [12] is a special case of SCR where the superstep size s is equal to identity.…”

“…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.…”