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A Very Practical Algorithm for the Two-Paths Problem in 3-Connected Planar Graphs

  • Torben Hagerup
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4769)

Abstract

A linear-time algorithm that does not need a planar embedding is presented for the problem of computing two vertex-disjoint paths, each with prescribed endpoints, in an undirected 3-connected planar graph.

Keywords

Planar Graph Linear Time Input Graph Tree Decomposition Practical Algorithm 
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.

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References

  1. 1.
    Fortune, S., Hopcroft, J., Wyllie, J.: The directed subgraph homeomorphism problem. Theoret. Comput. Sci. 10, 111–121 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Harary, F.: Graph Theory. Addison-Wesley, Reading, Mass (1969)Google Scholar
  3. 3.
    Kramer, M.R., van Leeuwen, J.: The complexity of wire-routing and finding minimum area layouts for arbitrary VLSI circuits. In: Preparata, F.P. (ed.) Advances in Computing Research, vol. 2, pp. 129–146. JAI Press, Greenwich, Conn (1984)Google Scholar
  4. 4.
    Lynch, J.F.: The equivalence of theorem proving and the interconnection problem. ACM SIGDA Newsletter 5, 31–36 (1975)CrossRefGoogle Scholar
  5. 5.
    Perković, L., Reed, B.: An improved algorithm for finding tree decompositions of small width. Internat. J. Foundat. Comput. Sci. 11, 365–371 (2000)CrossRefGoogle Scholar
  6. 6.
    Perl, Y., Shiloach, Y.: Finding two disjoint paths between two pairs of vertices in a graph. J. ACM 25, 1–9 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Robertson, N., Seymour, P.D.: Graph Minors. XIII. The disjoint paths problem. J. Comb. Theory, Ser. B 63, 65–110 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Schrijver, A.: Finding k disjoint paths in a directed planar graph. SIAM J. Comput. 23, 780–788 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Shiloach, Y.: A polynomial solution to the undirected two paths problem. J. ACM 27, 445–456 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Tholey, T.: Solving the 2-disjoint paths problem in nearly linear time. Theory Comput. Systems 39, 51–78 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Woeginger, G.: A simple solution to the two paths problem in planar graphs. Inform. Process. Lett. 36, 191–192 (1990)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Torben Hagerup
    • 1
  1. 1.Institut für Informatik, Universität Augsburg, 86135 AugsburgGermany

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