Skip to main content
SpringerLink
Log in

A parallel algorithm for the maximal path problem

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

In this paper we present anO (log5 n) time parallel algorithm for constructing a Maximal Path in an undirected graph. We also give anO (log1/2+ε) time parallel algorithm for constructing a depth first search tree in an undirected graph.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Anderson andE. Mayr, Parallelism and greedy algorithms,Technical Report No. STAN CS-84-1003, Computer Science Department, Stanford University, April 1984.

  2. R. Anderson andE. Mayr, Parallelism and the maximal path problem,Information Processing Letters,24 (1987), 121–126.

    Article  MATH  MathSciNet  Google Scholar 

  3. S. A. Cook, A taxonomy of problems with fast parallel algorithms,Information and Control,64 (1985), 2–22.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. Fortune andJ. Willie, Parallelism in random access machines,Proc. 10th ACM STOC (1978), 114–118.

  5. H. Gabow,Private communication, 1985.

  6. R. M. Karp, E. Upfal andA. Wigderson, Constructing a maximum matching is in random NC,Combinatorica,6 (1986), 35–48.

    MATH  MathSciNet  Google Scholar 

  7. R. M. Karp andA. Wigderson, A fast parallel algorithm for the maximal independent set problem,JACM,32 (4) (1985), 762–773.

    Article  MATH  MathSciNet  Google Scholar 

  8. K. Mulmuley, U. Vazarani andV. Vazarani, Matching is as easy as matrix inversion,Combinatorica,7 (1987), 105–113.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Reif. Depth first search is inherently sequential,Information Processing Letters,20 (1985), 229–234.

    Article  MATH  MathSciNet  Google Scholar 

  10. R. E. Tarján andU. Vishkin, Finding biconnected components and computing tree function in logarithmic parallel time,Proc. 25th FOCS, (1984) 12–20.

  11. U. Vishkin, An optimal parallel connectivity algorithm,RC 9149, IBM T.J. Watson Research Center, Yorktown Heights, N. Y., 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Washington, 98195, Seattle, Washington

    Richard Anderson

Authors
  1. Richard Anderson
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported in part by an IBM Faculty Development Award, an NSF Graduate Fellowship, and NSF grant DCR-8351757.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anderson, R. A parallel algorithm for the maximal path problem. Combinatorica 7, 315–326 (1987). https://doi.org/10.1007/BF02579320

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02579320

AMS subject classification (1980)

Search

Navigation