Dynamic programming on intervals

  • Takao Asano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 557)


We consider problems on intervals which can be solved by dynamic programming. Specifically, we give an efficient implementation of dynamic programming on intervals. As an application, an optimal sequential partition of a graph G=(V, E) can be obtained in O(m log n) time, where n = ¦V¦ and m = ¦E¦. We also present an O(n log n) time algorithm for finding a minimum weight dominating set of an interval graph G=(V, E), and an O(m log n) time algorithm for finding a maximum weight clique of a circular-arc graph G=(V, E), provided their intersection models of n intervals (arcs) are given.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    T. Asano, An faster algorithm for finding a maximum weight clique of a circular-arc graph, Technical Report of Institut für Operations Research, Universität Bonn, 90624-OR, 1990.Google Scholar
  2. [2]
    J.L. Bentley, Decomposable searching problems, Information Processing Letters, 8 (1979), pp. 244–251.Google Scholar
  3. [3]
    A.A. Bertossi and S. Moretti, Parallel algorithms on circular-arc graphs Information Processing Letters, 33 (1989/1990), pp. 275–281.Google Scholar
  4. [4]
    W.-L. Hsn, Maximum weight clique algorithms for circular-arc graphs and circle graphs, SIAM Journal on Computing, 14 (1985), pp. 224–231.Google Scholar
  5. [5]
    T. Kaji and A. Ohuchi, Optimal sequential partitions of graphs by branch and bound, Technical Report 90-AL-10, Information Processing Society of Japan, 1990.Google Scholar
  6. [6]
    B.W. Kernighan, Optimal sequential partitions of graphs, Journal of ACM, 18 (1971), pp. 34–40.Google Scholar
  7. [7]
    F.P. Preparata and M.I. Shamos, Computational Geometry: An Intorduction, Springer-Verlag, New York, 1985.Google Scholar
  8. [8]
    W.-K. Shih and W.-L. Hsu, An O(n log n+m loglog n) maximum weight clique algorithm for circular-arc graphs, Information Processing Letters, 31 (1989), pp. 129–134.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Takao Asano
    • 1
  1. 1.Department of Mechanical EngineeringSophia UniversityTokyoJapan

Personalised recommendations