The Longest Path Problem Is Polynomial on Interval Graphs

Authors:
Kyriaki Ioannidou;George B. Mertzios;Stavros D. Nikolopoulos
Affiliations:
Department of Computer Science, University of Ioannina, Greece;Department of Computer Science, RWTH Aachen University, Germany;Department of Computer Science, University of Ioannina, Greece
Venue:
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Year:
2009

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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.