Advertisement

Algorithms for finding non-crossing paths with minimum total length in plane graphs

  • Jun-ya Takahashi
  • Hitoshi Suzuki
  • Takao Nishizeki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 650)

Abstract

Let G be an undirected plane graph with non-negative edge length, and let k terminal pairs lie on two specified face boundaries. This paper presents an algorithm for finding k “non-crossing paths” in G, each connecting a terminal pair, whose total length is minimum. Here “non-crossing paths” may share common vertices or edges but do not cross each other in the plane. The algorithm runs in time O(n log n) where n is the number of vertices in G.

Keywords

Short Path Grid Graph Face Boundary Middle Generation Terminal Pair 
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. [AHU]
    A.V. Aho, J. E. Hopcroft and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA (1974).Google Scholar
  2. [Fre]
    G. N. Frederickson, Fast algorithms for shortest path in planar graphs, with applications, SIAM J. Compnt., 16, pp. 1004–1022 (1987).CrossRefGoogle Scholar
  3. [GT]
    H. N. Gabow and R. E. Tarjan, A linear-time algorithm for a special case of disjoint set union, Journal of Computer and System Sciences, 30, pp. 209–221 (1985).Google Scholar
  4. [KL]
    M. R. Kramer and J. van Leewen, Wire-routing is NP-complete, Report No. RUU-CS-82-4, Department of Computer Science, University of Utrecht, Utrecht, the Netherlands (1982).Google Scholar
  5. [Lyn]
    J. F. Lynch, The equivalence of theorem proving and the interconnection problem, ACM SIGDA, The Netherlands (1982).Google Scholar
  6. [SAN]
    H. Suzuki, T. Akama and T. Nishizeki, Finding Steiner forests in planar graphs, Proc. of First Siam-ACM Soda, pp. 444–453 (1990).Google Scholar
  7. [Tar]
    R.E. Tarjan, Data Structures and Network Algorithms, SIAM, Philadelphia, PA (1983).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Jun-ya Takahashi
    • 1
  • Hitoshi Suzuki
    • 1
  • Takao Nishizeki
    • 1
  1. 1.Department of Information Engineering Faculty of EngineeringTohoku UniversitySendaiJapan

Personalised recommendations