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All graphs have cycle separators and planar directed depth-first search is in DNC

  • NC Algorithms
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VLSI Algorithms and Architectures (AWOC 1988)

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

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Abstract

All graphs have cycle separators. (A single vertex is regarded as a trivial cycle.) In sequential computation, a cycle separator can be found in O(n + e) time for any undirected graph of n vertices and e edges; in O((n + e) log n) time for any directed graph. In parallel computation, it is in deterministic NC to convert any depth-first search forest of any graph into a cycle separator. Moreover, finding a cycle separator for any planar directed graph is in deterministic NC; consequently, finding a depth-first search forest in any planar directed graph is in deterministic NC, too.

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supported in part by a 1987 Summer Faculty Fellowship from Indiana University at Bloomington.

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References

  1. Alok Aggarwal and Richard J. Anderson. A random NC algorithm for depth first search. In ACM Symposium on Theory of Computing, pages 325–334, 1987.

    Google Scholar 

  2. Alok Aggarwal, Richard J. Anderson, and Ming Y. Kao. Parallel depth-first search in directed graphs. Manuscript, February 1988.

    Google Scholar 

  3. Greg N. Frederickson and Ravi Janardan. Separator-based strategies for efficient message routing. In IEEE Symposium on Foundations of Computer Science, pages 428–437, 1986.

    Google Scholar 

  4. Ratan K. Ghosh and G. P. Bhattacharjee. A parallel search algorithm for directed acyclic graphs. BIT, 24:134–150, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  5. Hillel Gazit and Gary L. Miller. A parallel algorithm for finding a separator in planar graphs. In IEEE Symposium on Foundations of Computer Science, pages 238–248, 1987.

    Google Scholar 

  6. Andrew V. Goldberg, Serge A. Plotkin, and Gregory E. Shannon. Parallel symmetry-breaking in sparse graphs. In ACM Symposium on Theory of Computing, pages 315–324, 1987.

    Google Scholar 

  7. Donald B. Johnson and Shankar M. Venkatesan. Partition on planar flow networks. In IEEE Symposium on Foundations of Computer Science, pages 259–264, 1983.

    Google Scholar 

  8. Philip N. Klein and John H. Reif. An efficient parallel algorithm for planarity. In IEEE Symposium on Foundations of Computer Science, pages 465–477, 1986.

    Google Scholar 

  9. Clyde P. Kruskal, Larry Rudolph, and Marc Snir. The power of parallel prefix. IEEE Transactions on Computers, c-34(10):965–968, October 1985.

    Google Scholar 

  10. Charles E. Leiserson. Area-efficient graph layouts (for VLSI). In IEEE Symposium on Foundations of Computer Science, pages 270–281, 1980.

    Google Scholar 

  11. L. Lovász. Computing ears and branchings. In IEEE Symposium on Foundations of Computer Science, pages 464–467, 1985.

    Google Scholar 

  12. R.J. Lipton, D.J. Rose, and R.E. Tarjan. Generalized nested dissection. SIAM Journal of Numerical Analysis, 16:346–358, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  13. R.J. Lipton and R.E. Tarjan. A separator theorem for planar graphs. SIAM Journal of Applied Mathematics, 36:177–189, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  14. Gary L. Miller. Finding small simple cycle separators for 2-connected planar graphs. In ACM Symposium on Theory of Computing, pages 376–382, 1984.

    Google Scholar 

  15. Victor Pan and John Reif. Fast and Efficient Solution of Path Algebra Problems. Technical Report 3, Computer Science Department, State University of New York at Albany, 1987.

    Google Scholar 

  16. John H. Reif. Depth-first search is inherently sequential. Information Processing Letters, 20:229–234, June 1985.

    Article  MATH  MathSciNet  Google Scholar 

  17. Justin R. Smith. Parallel algorithms for depth first searchs I. planar graphs. SIAM Journal of Computing, 15(3):814–830, August 1986.

    Article  MATH  Google Scholar 

  18. Catherine A. Schevon and Jeffrey Scott Vitter. A Parallel Algorithm for Recognizing Unordered Depth-First Search. Technical Report 21, Department of Computer Science, Brown University, 1985.

    Google Scholar 

  19. L.G. Valiant. Universality considerations in 'VLSI circuits. IEEE Transactions on Computers, 30(2):135–140, February 1981.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Indiana University, 47405, Bloomington, IN

    Ming-Yang Kao

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  1. Ming-Yang Kao
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John H. Reif

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© 1988 Springer-Verlag Berlin Heidelberg

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Kao, MY. (1988). All graphs have cycle separators and planar directed depth-first search is in DNC. 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/BFb0040373

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  • DOI: https://doi.org/10.1007/BFb0040373

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96818-6

  • Online ISBN: 978-0-387-34770-7

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