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Finding edge-disjoint paths in partial k-trees

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Book cover Algorithms and Computation (ISAAC 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1178))

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Abstract

For a given graph G and p pairs (s i, ti), 1≤i≤p, of vertices in G, the edge-disjoint paths problem is to find p pairwise edge-disjoint paths P i, 1≤i≤p, connecting s i and t i. Many combinatorial problems can be efficiently solved for partial k-trees (graphs of treewidth bounded by a fixed integer k), but it has not been known whether the edge-disjoint paths problem can be solved in polynomial time for partial k-trees unless p=O(1). This paper gives two algorithms for the edge-disjoint paths problem on partial k-trees. The first one solves the problem for any partial k-tree G and runs in polynomial time if p=O(log n) and in linear time if p=O(1), where n is the number of vertices in G. The second one solves the problem under some restriction on the location of terminal pairs even if p ≥ log n.

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Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, 980-77, Sendai, Japan

    Xiao Zhou, Syurei Tamura & Takao Nishizeki

Authors
  1. Xiao Zhou
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  2. Syurei Tamura
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  3. Takao Nishizeki
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Editor information

Tetsuo Asano Yoshihide Igarashi Hiroshi Nagamochi Satoru Miyano Subhash Suri

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© 1996 Springer-Verlag Berlin Heidelberg

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Zhou, X., Tamura, S., Nishizeki, T. (1996). Finding edge-disjoint paths in partial k-trees. In: Asano, T., Igarashi, Y., Nagamochi, H., Miyano, S., Suri, S. (eds) Algorithms and Computation. ISAAC 1996. Lecture Notes in Computer Science, vol 1178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009496

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  • DOI: https://doi.org/10.1007/BFb0009496

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62048-8

  • Online ISBN: 978-3-540-49633-5

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