Advertisement

Efficient parallel algorithms for some tree layout problems

  • J. Díaz
  • A. Gibbons
  • G. Pantziou
  • M. Serna
  • P. Spirakis
  • J. Toran
Session 6A: Parallel Alg./Learning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)

Abstract

The minimum cut and minimum length linear arrangement problems usually occur in solving wiring problems and have a lot in common with job sequencing questions. Both problems are NP-complete for general graphs and in P for trees. We present here two parallel algorithms for the CREW PRAM. The first solves the minimum length linear arrangement problem for trees and the second solves the minimum cut arrangement for trees. We prove that the first problem belongs to NC for trees, and the second problem also is in NC for bounded degree trees.

Keywords

Parallel Algorithm Polynomial Time Algorithm Tree Decomposition Layout Problem Optimal Layout 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [ADKP89]
    K. Abrahamson, N. Dadoun, D. Kirkpatrick, and K. Przytycka. A simple parallel tree contraction algorithm. Journal of Algorithms, 10:287–302, 1989.CrossRefGoogle Scholar
  2. [AH73]
    D. Adolphson and T.C. Hu. Optimal linear ordering. SIAM J. on Applied Mathematics, 25(3):403–423, Nov 1973.CrossRefGoogle Scholar
  3. [CMST82]
    M. Chung, F. Makedon, I.H. Sudborough, and J. Turner. Polynomial time algorithms for the min cut problem on degree restricted trees. In FOCS, volume 23, pages 262–271, Chicago, Nov 1982.Google Scholar
  4. [Di92]
    J. Díaz. Graph layout problems. In I.M. Havel and V. Koubek, editors, Mathematical Foundations of Computer Science, volume 629, pages 14–24. Springer-Verlag, Lecture Notes in Computer Science, 1992.Google Scholar
  5. [ES78]
    S. Even and Y. Shiloach. NP-completeness of several arrangements problems. Technical report, TR-43 The Technical, Haifa, 1978.Google Scholar
  6. [Gav77]
    F. Gavril. Some NP-complete problems on graphs. In Proc. 11th. Conf. on Information Sciences and Systems, pages 91–95, John Hopkins Univ., Baltimore, 1977.Google Scholar
  7. [GJ79]
    M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to Oie Theory of NP-Completeness. Freeman, San Francisco, 1979.Google Scholar
  8. [Har66]
    L.H. Harper. Optimal numberings and isoperimetric problems on graphs. Journal of Combinatorial Theory, 1(3):385–393, 1966.Google Scholar
  9. [MS86]
    B. Monien and I.H. Sudborough. Min cut is NP-complete for edge weighted trees. In L. Kott, editor, Proc. 13th. Coll. on Automata, Languages and Programming, pages 265–274. Springer-Verlag, Lectures Notes in Computer Science, 1986.Google Scholar
  10. [SH86]
    M.T. Shing and T. C. Hu. Computational complexity of layout problems. In T. Ohtsuki, editor, Layout design and verification, pages 267–294, Amsterdam, 1986. North-Holland.Google Scholar
  11. [Shi79]
    Yossi Shiloach. A minimum linear arrangement algorithm for undirected trees. SIAM J. on Computing, 8(1):15–31, February 1979.CrossRefGoogle Scholar
  12. [Yan83]
    Mihalis Yannakakis. A polynomial algorithm for the min cut linear arrangement of trees. In IEEE Symp. on Found. of Comp. Sci., volume 24, pages 274–281, Providence RI, Nov. 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • J. Díaz
    • 1
  • A. Gibbons
    • 2
  • G. Pantziou
    • 3
    • 4
  • M. Serna
    • 1
  • P. Spirakis
    • 4
    • 5
  • J. Toran
    • 1
  1. 1.Departament de Llenguatges i SistemesUniversitat Politècnica CatalunyaUSA
  2. 2.Department of Computer ScienceUniversity of WarwickUSA
  3. 3.University of Central FloridaUSA
  4. 4.Computer Technology InstituteUSA
  5. 5.University of PatrasUSA

Personalised recommendations