The MINSUMCUT problem

  • J. Díaz
  • A. M. Gibbons
  • M. S. Paterson
  • J. Torán
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 519)


In this paper we first present a sequential linear algorithm for a linear arrangement problem on trees, MINSUMCUT, and then an O(log n)-time parallel algorithm for MINSUMCUT on trees, which uses n2/(logn) processors.


Parallel Algorithm Directed Edge Sequential Algorithm Linear Arrangement Outerplanar Graph 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AH73]
    D. Adolphson and T.C. Hu. Optimal linear ordering. SIAM J. on Applied Mathematics, 25(3):403–423, Nov 1973.Google Scholar
  2. [Dia79]
    J. Diaz. The δ-operator. In L. Budach, editor, Fundamentals of Computation Theory, pages 105–111. Akademie-Verlag, 1979.Google Scholar
  3. [GGJK78]
    M.R. Garey, R.L. Graham, D.S. Johnson, and D. Knuth. Complexity results for bandwidth minimization. SIAM J on Applied Mathematics, 34:477–495, Sept. 1978.Google Scholar
  4. [GJ76]
    M.R. Garey and D.S. Johnson. Some simplified NP-complete graph problems. Theoretical Computer Science, 1:237–267, 1976.Google Scholar
  5. [GJ79]
    M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, 1979.Google Scholar
  6. [GR88]
    A. Gibbons and W. Rytter. Efficient Parallel Algorithms. Cambridge University Press, Cambridge, 1988.Google Scholar
  7. [GR89]
    A. Gibbons and W. Rytter. Optimal parallel algorithms for dynamic expression evaluation and context free recognition. Information and Computation, 81(1):32–45, April 1989.Google Scholar
  8. [GR90]
    A. Gibbons and W. Rytter. Optimal edge-colouring outerplanar graphs is in NC. Theoretical Computer Science, 71:401–411, 1990.Google Scholar
  9. [Har77]
    L.H. Harper. Stabilization and the edgesum problem. Ars Combinatoria, 4:225–270, Dec. 1977.Google Scholar
  10. [NK72]
    M. Nanan and M. Kurtzberg. A review of the placement and quadratic assignment problems. SIAM Review, 14(2):324–341, April 1972.Google Scholar
  11. [Shi79]
    Yossi Shiloach. A minimum linear arrangement algorithm for undirected trees. SIAM J. on Computing, 8(1):15–31, February 1979.Google 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 1991

Authors and Affiliations

  • J. Díaz
    • 1
  • A. M. Gibbons
    • 2
  • M. S. Paterson
    • 2
  • J. Torán
    • 1
  1. 1.Departament de Llenguates i SistemesUniversitat Politècnica CatalunyaBarcelonaSpain
  2. 2.Department of Computer ScienceUniversity of WarwickCoventryUK

Personalised recommendations