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Algorithmica

, Volume 61, Issue 2, pp 320–341 | Cite as

The Longest Path Problem has a Polynomial Solution on Interval Graphs

  • Kyriaki Ioannidou
  • George B. Mertzios
  • Stavros D. Nikolopoulos
Article

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 (Proc. of the 15th Annual International Symp. on Algorithms and Computation (ISAAC), LNCS, vol. 3341, pp. 871–883, 2004), 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 uses a dynamic programming approach and runs in O(n 4) time, where n is the number of vertices of the input graph.

Keywords

Longest path problem Interval graphs Polynomial algorithm Complexity Dynamic programming 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Kyriaki Ioannidou
    • 1
  • George B. Mertzios
    • 2
  • Stavros D. Nikolopoulos
    • 1
  1. 1.Department of Computer ScienceUniversity of IoanninaIoanninaGreece
  2. 2.Department of Computer ScienceRWTH Aachen UniversityAachenGermany

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