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International Symposium on Mathematical Foundations of Computer Science

MFCS 2009: Mathematical Foundations of Computer Science 2009 pp 403–414Cite as

The Longest Path Problem Is Polynomial on Interval Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5734))

Abstract

The longest path problem is the problem of finding a path of maximum length in a graph. Polynomial solutions for this problem are known only for small classes of graphs, while it is NP-hard on general graphs, as it is a generalization of the Hamiltonian path problem. Motivated by the work of Uehara and Uno in [20], where they left the longest path problem open for the class of interval graphs, in this paper we show that the problem can be solved in polynomial time on interval graphs. The proposed algorithm runs in O(n 4) time, where n is the number of vertices of the input graph, and bases on a dynamic programming approach.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Ioannina, Greece

    Kyriaki Ioannidou & Stavros D. Nikolopoulos

  2. Department of Computer Science, RWTH Aachen University, Germany

    George B. Mertzios

Authors
  1. Kyriaki Ioannidou
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  2. George B. Mertzios
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  3. Stavros D. Nikolopoulos
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Faculty of Mathematics, Physics and Informatics, Comenius University, Research partially funded by grant APVV 0433-06, Bratislava, Slovakia

    Rastislav Královič

  2. Members of EACSL Jury for the Ackermann Award, Poland

    Damian Niwiński

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© 2009 Springer-Verlag Berlin Heidelberg

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Ioannidou, K., Mertzios, G.B., Nikolopoulos, S.D. (2009). The Longest Path Problem Is Polynomial on Interval Graphs. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_35

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  • DOI: https://doi.org/10.1007/978-3-642-03816-7_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03815-0

  • Online ISBN: 978-3-642-03816-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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