, Volume 5, Issue 1-4, pp 43-64

Efficient parallel algorithms for graph problems

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We present an efficient technique for parallel manipulation of data structures that avoids memory access conflicts. That is, this technique works on the Exclusive Read/Exclusive Write (EREW) model of computation, which is the weakest shared memory, MIMD machine model. It is used in a new parallel radix sort algorithm that is optimal for keys whose values are over a small range. Using the radix sort and known results for parallel prefix on linked lists, we develop parallel algorithms that efficiently solve various computations on trees and “unicycular graphs.” Finally, we develop parallel algorithms for connected components, spanning trees, minimum spanning trees, and other graph problems. All of the graph algorithms achieve linear speedup for all but the sparsest graphs.

Part of this work was done while the first author was at the University of Illinois, Urbana-Champaign, the second author was at Carnegie-Mellon University, and the third author was at the Hebrew University and the Courant Institute of Mathematical Sciences, New York University. A preliminary version of this work was presented at the 1986 International Conference on Parallel Processing.
Communicated by F. Thomson Leighton.