Parallel Graph Algorithms for Coarse-Grained Multicomputers

Abstract

Current applications in parallel machines are restricted to trivially parallelizable problems. In real machines communication time is often much greater than cornputation time. Therefore for many non-trivial graph problems, many theoretically efficient parallel algorithms for PRAM or fine grained network models often give disappointing speedups when implemented on real machines. The CGM (Coarse Grained Multicomputer) model was proposed by F. Dehne to be an adequate model of parallelism sufficiently close to existing parallel machines. It is a simple model but nevertheless intends to give a reasonable prediction of performance when parallel algorithms on this model are implemented. CGM algorithms are expected to have theoretical complexity analyses close to actual times observed in real implementations. In this chapter we present the CGM model and discuss several CGM scalable parallel algorithms to solve some basic graph problems, including connected components and list ranking. It is important to have very efficient algorithms for such basic problems because, as shown by J. H. Reif, many important graph problems are based on these subproblems.