, Volume 5, Issue 1, pp 43–64

Efficient parallel algorithms for graph problems

  • Clyde P. Kruskal
  • Larry Rudolph
  • Marc Snir

DOI: 10.1007/BF01840376

Cite this article as:
Kruskal, C.P., Rudolph, L. & Snir, M. Algorithmica (1990) 5: 43. doi:10.1007/BF01840376


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.

Key words

Biconnected componentsConnected componentsMinimum spanning treesParallel algorithmsParallel processingPRAMRadix sortSpanning treesTree computations

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Clyde P. Kruskal
    • 1
  • Larry Rudolph
    • 2
  • Marc Snir
    • 3
  1. 1.Computer Science DepartmentUniversity of MarylandCollege ParkUSA
  2. 2.Institute of Mathematics and Computer ScienceThe Hebrew University of JerusalemJerusalemIsrael
  3. 3.IBM T. J. Watson Research CenterYorktown HeightsUSA