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The longest path problem is polynomial on interval graphs.

Ioannidou, K. and Mertzios, G.B. and Nikolopoulos, S.D. (2009) 'The longest path problem is polynomial on interval graphs.', in Mathematical foundations of computer science 2009 34th international symposium, MFCS 2009, Novy Smokovec, High Tatras, Slovakia, August 24-28, 2009 : proceedings. Berlin, Heidelberg: Springer, pp. 403-414. Lecture notes in computer science. (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.

Item Type:Book chapter
Additional Information:Symposium URL: http://www.mfcs.sk/mfcs2009/
Keywords:Longest path problem, Interval graphs, Polynomial algorithm, Complexity, Dynamic programming.
Full text:PDF (Copyright agreement prohibits open access to the full-text) - Accepted Version
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1007/978-3-642-03816-7_35
Record Created:22 Feb 2012 15:35
Last Modified:09 Oct 2014 10:51

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