Skip to main content
SpringerLink
Log in

Subtree isomorphism is in random NC

  • NC Algorithms
  • Conference paper
  • First Online:
VLSI Algorithms and Architectures (AWOC 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 319))

Included in the following conference series:

Abstract

Given two trees, a guest tree G and a host tree H, the subtree isomorphism problem is to determine whether there is a subgraph of H that is isomorphic to G. We present a randomized parallel algorithm for finding such an isomorphism, if it exists. The algorithm runs in time O(log3 n) on a CREW PRAM, where n is the number of nodes in H. Randomization is used (solely) to solve each of a series of bipartite matching problems during the course of the algorithm. We demonstrate the close connection between the two problems by presenting a log space reduction from bipartite perfect matching to subtree isomorphism. Finally, we present some techniques to reduce the number of processors used by the algorithm.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Borodin, J. von zur Gathen, and J. Hopcroft. Fast parallel matrix and GCD computations. In Proc. of the Symp. on Foundations of Computer Science (FOCS), Oct. 1982.

    Google Scholar 

  2. R. Brent. The parallel evaluation of general arithmetic expressions. JACM, 21:201–208, 1974.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Edmonds. Systems of distinct representatives and linear algebra. J. Res. Nat. Bureau of Standards, 71B:241–245, 1967.

    MathSciNet  Google Scholar 

  4. A. Lingas and M. Karpinski. Subtree isomorphism and bipartite perfect matching are mutually NC reducible. 1987. submitted for publication.

    Google Scholar 

  5. D. W. Matula. Subtree isomorphism in O(n 5/2). Annals of Discrete Mathematics, 2:91–106, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  6. G. L. Miller and J. H. Reif. Parallel tree contraction and its applications. In Proc. of the Symp. on Foundations of Computer Science (FOCS), Oct. 1985.

    Google Scholar 

  7. K. Mulmuley, U. Vazirani, and V. Vazirani. Matching is as easy as matrix inversion. Combinatorica, 7(1):105–113, 1987.

    MATH  MathSciNet  Google Scholar 

  8. F. Preparata and D. Sarwate. An improved parallel processor bound in fast matrix inversion. Information Processing Letters, 7(3):148–150, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. O. Rabin and V. V. Vazirani. Maximum Matchings in General Graphs through Randomization. Technical Report TR-15-84, Aiken Computation Laboratory, Harvard University, Oct. 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of California, Berkeley

    Phillip B. Gibbons, Richard M. Karp & Danny Soroker

  2. University of Southern, California

    Gary L. Miller

Authors
  1. Phillip B. Gibbons
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gary L. Miller
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Richard M. Karp
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Danny Soroker
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

John H. Reif

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gibbons, P.B., Miller, G.L., Karp, R.M., Soroker, D. (1988). Subtree isomorphism is in random NC. In: Reif, J.H. (eds) VLSI Algorithms and Architectures. AWOC 1988. Lecture Notes in Computer Science, vol 319. Springer, New York, NY. https://doi.org/10.1007/BFb0040372

Download citation

  • DOI: https://doi.org/10.1007/BFb0040372

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96818-6

  • Online ISBN: 978-0-387-34770-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation