, Volume 8, Issue 1, pp 1–12 | Cite as

A random 1-011-011-01algorithm for depth first search

  • A. Aggarwal
  • R. J. Anderson


In this paper we present a fast parallel algorithm for constructing a depth first search tree for an undirected graph. The algorithm is anRNC algorithm, meaning that it is a probabilistic algorithm that runs in polylog time using a polynomial number of processors on aP-RAM. The run time of the algorithm isO(TMM(n) log3n), and the number of processors used isPMM (n) whereTMM(n) andPMM(n) are the time and number of processors needed to find a minimum weight perfect matching on ann vertex graph with maximum edge weightn.

AMS subject classifications (1980)

68 Q 10 05 C 99 


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  1. [1]
    R. J. Anderson, A parallel algorithm for the maximal path problem,Combinatorica,7 (1987), 315–326.Google Scholar
  2. [2]
    R. J.Anderson, A parallel algorithm for depth-first search,Extended Abstract, Math. Science Research Institute (1986).Google Scholar
  3. [3]
    R. J.Anderson and E.Mayr, Parallelism and greedy algorithms,Technical Report No. STAN-CS-84-1003,Computer Science Department, Stanford University (1984).Google Scholar
  4. [4]
    S. A. Cook, A taxonomy of problems with fast parallel algorithms,Information and Control,64 (1985), 2–22.Google Scholar
  5. [5]
    D.Eckstein and D.Alton, Parallel graph processing using depth first search,Proc. of the Conf. on Theoretical Computer Science at the Univ. of Waterloo, (1977), 21–29.Google Scholar
  6. [6]
    S. Even andR. E. Tarjan, Network flow and testing graph connectivity,SIAM Journal of Computing,4 (1975), 507–518.Google Scholar
  7. [7]
    R. K. Ghosh andG. P. Bhattacharjee, A parallel search algorithm for directed acyclic graphs,BIT,24 (1984), 134–150.Google Scholar
  8. [8]
    R. M. Karp, E. Upfal andA. Wigderson, Constructing a maximum matching is in randomNC, Combinatorica,6 (1986), 35–48.Google Scholar
  9. [9]
    R. M. Karp andA. Wigderson, A fast parallel algorithm for the maximal independent set problem,Journal of ACM,32 (1985), 762–773.Google Scholar
  10. [10]
    R. J. Lipton andR. E. Tarjan, A separator theorem for planar graphs,SIAM Journal of Applied Math. 36 (1979), 177–189.Google Scholar
  11. [11]
    K. Mulmuley, U. V. Vazirani andV. V. Vazirani, Matching is as easy as matrix inversion,Combinatorica 7 (1986), 105–114.Google Scholar
  12. [12]
    V.Ramachandran,Personal Communication.Google Scholar
  13. [13]
    E. Reghbati andD. Corneil, Parallel computations in graph theory,SIAM Journal of Computing,7 (1978), 230–237.Google Scholar
  14. [14]
    J. H. Reif, Depth-first search is inherently sequential,Information Processing Letters,20 (1985), 229–234.Google Scholar
  15. [15]
    J. R. Smith, Parallel algorithms for depth first searches,SIAM Journal of Computing,15 (1986), 814–830.Google Scholar
  16. [16]
    R. E. Tarjan, Depth-first search and linear graph algorithms,SIAM J. of Computing,1 (1972), 146–160.Google Scholar
  17. [17]
    J. C.Wyllie,The Complexity of Parallel Computations, Phd. Thesis, Department of Computer Science, Cornell University, 1979.Google Scholar

Copyright information

© Akadémiai Kiadó 1988

Authors and Affiliations

  • A. Aggarwal
    • 1
  • R. J. Anderson
    • 2
  1. 1.IBM T. J. Watson CenterYorktown HeightsUSA
  2. 2.Dept. of Computer Science, FR-35University of WashingtonSeattleUSA

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