Efficient parallel graph algorithms based on open ear decomposition

  • Louis Ibarra
  • Dana Richards
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)


We present a new technique called ”disjoint decreasing ear paths”, which is based on a graph's open ear decomposition. We apply this technique in CRCW PRAM parallel algorithms for the two vertex disjoint s — t paths problem and the maximal path problem in planar graphs. These run in O(log n) time with n + m processors and O(log2n) time with O(n) processors, respectively, where the graph has n vertices and m edges.


Planar Graph Parallel Algorithm Internal Vertex Maximal Path Biconnected Graph 
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  1. 1.
    R. Anderson. A parallel algorithm for the maximal path problem. Combinatorica, 7:315–326, 1987.Google Scholar
  2. 2.
    R. Anderson and E. Mayr. Parallelism and the maximal path problem. Information Processing Letters, 24:121–126, 1987.Google Scholar
  3. 3.
    J. Bondy and U. Murty. Graph Theory with Applications. North-Holland, Amsterdam, 1976.Google Scholar
  4. 4.
    R. Cole and U. Vishkin. Approximate parallel scheduling ii: Applications to logarithmic-time optimal parallel graph algorithms. Information and Computation, 92:1–47, 1991.Google Scholar
  5. 5.
    T. H. Corman, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press and McGraw-Hill Book Co., Cambridge, MA and New York, NY, 1990.Google Scholar
  6. 6.
    D. Fussell, V. Ramachandran, and R. Thurimella. Finding triconnected components by local replacements. In Proc. 16th ICALP, Lecture Notes in Computer Science 372, pages 379–393, New York, 1989. Springer-Verlag.Google Scholar
  7. 7.
    X. He and Y. Yesha. A nearly optimal parallel algorithm for constructing depth first search trees in planar graphs. SIAM Journal on Computing, 17(3):486–491, 1988.Google Scholar
  8. 8.
    L. Ibarra and D. Richards. Efficient parallel algorithms based on open ear decompositions. Submitted to Parallel Computing.Google Scholar
  9. 9.
    A. Kanevsky and V. Ramachandran. Improved algorithms for four-connectivity. Journal of Computer and System Sciences, 42:288–306, 1991.Google Scholar
  10. 10.
    S. Khuller. Ear decompositions. SigAct News, 20(1):128, 1989.Google Scholar
  11. 11.
    S. Khuller and B. Schieber. Efficient parallel algorithms for testing connectivity and finding disjoint s-t paths in graphs. In Proc. 30th Annual IEEE Symp. on Foundations of Computer Science, pages 288–293, 1989.Google Scholar
  12. 12.
    L. Lovász. Computing ears and branchings in parallel. In Proc. 26th Annual IEEE Symp. on Foundations of Computer Science, pages 464–467, 1985.Google Scholar
  13. 13.
    Y. Maon, B. Schieber, and U. Vishkin. Parallel ear decomposition search (eds) and stnumbering in graphs. Theoretical Computer Science, 47:277–298, 1986.Google Scholar
  14. 14.
    G. L. Miller and V. Ramachandran. A new graph triconnectivity algorithm and its parallelization. In Proc. 19th Annual ACM Symp. on Theory of Computing, pages 335–344, 1987.Google Scholar
  15. 15.
    V. Ramachandran and J. Reif. An optimal parallel algorithm for graph planarity. In Proc. 30th Annual IEEE Symp. on Foundations of Computer Science, pages 282–287, 1989.Google Scholar
  16. 16.
    V. Ramachandran and U. Vishkin. Efficient parallel triconnectivity in logarithmic time. In 3rd Aegean Workshop on Computing, Lecture Notes in Computer Science 319, pages 33–42, New York, 1988. Springer-Verlag.Google Scholar
  17. 17.
    G. E. Shannon. A linear-processor algorithm for depth-first search in planar graphs. Information Processing Letters, 29:119–123, 1988.Google Scholar
  18. 18.
    R. E. Tarjan and U. Vishkin. An efficient parallel biconnectivity algorithm. SIAM Journal on Computing, 14(4):862–874, 1985.Google Scholar
  19. 19.
    U. Vishkin. Implementation of simultaneous memory address access in models that forbid it. Journal of Algorithms, 4(1):45–50, 1983.Google Scholar
  20. 20.
    H. Whitney. Non-separable and planar graphs. Transactions of the American Mathematical Society, 34:339–362, 1932.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Louis Ibarra
    • 1
  • Dana Richards
    • 2
  1. 1.Dept. of Computer ScienceRutgers UniversityNew Brunswick
  2. 2.Division of Computer and Computation ResearchNational Science FoundationWashington, D.C.

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