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Efficient Algorithms for the Longest Path Problem

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Algorithms and Computation (ISAAC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3341))

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Abstract

The longest path problem is to find a longest path in a given graph. While the graph classes in which the Hamiltonian path problem can be solved efficiently are widely investigated, very few graph classes are known where the longest path problem can be solved efficiently. For a tree, a simple linear time algorithm for the longest path problem is known. We first generalize the algorithm, and it then solves the longest path problem efficiently for weighted trees, block graphs, ptolemaic graphs, and cacti. We next propose three new graph classes that have natural interval representations, and show that the longest path problem can be solved efficiently on those classes. As a corollary, it is also shown that the problem can be solved efficiently on threshold graphs.

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Author information

Authors and Affiliations

  1. Department of Information Processing, School of Information Science, JAIST, Ishikawa, Japan

    Ryuhei Uehara

  2. Department of Mathematics and Information Science, College of Integrated Arts and Sciences, Osaka Prefecture University, Sakai, Japan

    Yushi Uno

Authors
  1. Ryuhei Uehara
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  2. Yushi Uno
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Fudan University, 200433, Shanghai, China

    Rudolf Fleischer

  2. Department of Computer Science, The Hong Kong University of Science and Technology, Hong Kong

    Gerhard Trippen

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© 2004 Springer-Verlag Berlin Heidelberg

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Uehara, R., Uno, Y. (2004). Efficient Algorithms for the Longest Path Problem. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_74

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  • DOI: https://doi.org/10.1007/978-3-540-30551-4_74

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24131-7

  • Online ISBN: 978-3-540-30551-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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