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The Disjoint Paths Problem: Algorithm and Structure

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Book cover WALCOM: Algorithms and Computation (WALCOM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6552))

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Abstract

We consider the following well-known problem, which is called the disjoint paths problem.

Input: A graph G with n vertices and m edges, k pairs of vertices (s 1,t 1),(s 2,t 2),..., (s k ,t k ) in G.

Output: (Vertex- or edge-) disjoint paths P 1, P 2, ...,P k in G such that P i joins s i and t i for i = 1,2,...,k.

This is certainly a central problem in algorithmic graph theory and combinatorial optimization. See the surveys [9, 31]. It has attracted attention in the contexts of transportation networks, VLSI layout and virtual circuit routing in high-speed networks or Internet. A basic technical problem is to interconnect certain prescribed “channels” on the chip such that wires belonging to different pins do not touch each other. In this simplest form, the problem mathematically amounts to finding vertex-disjoint trees or vertex-disjoint paths in a graph, each connecting a given set of vertices.

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Authors and Affiliations

  1. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan

    Ken-ichi Kawarabayashi

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  1. Ken-ichi Kawarabayashi
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Editors and Affiliations

  1. Department of Architecture and Architectural Engineering, Kyoto University, 615-8540, Nishikyo-ku, Kyoto, Japan

    Naoki Katoh

  2. Department of Computer Science and Engineering, Hauz Khas, Indian Institute of Technology, 11016, New Delhi, India

    Amit Kumar

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Kawarabayashi, Ki. (2011). The Disjoint Paths Problem: Algorithm and Structure. In: Katoh, N., Kumar, A. (eds) WALCOM: Algorithms and Computation. WALCOM 2011. Lecture Notes in Computer Science, vol 6552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19094-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-19094-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19093-3

  • Online ISBN: 978-3-642-19094-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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