The longest path problem is polynomial on interval graphs

Ioannidou, K.; Mertzios, G.B.; Nikolopoulos, S.D.

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.

Citation

Ioannidou, K., Mertzios, G., & Nikolopoulos, S. (2009, August). The longest path problem is polynomial on interval graphs. Presented at 34st International Symposium on Mathematical Foundations of Computer Science (MFCS), Novy Smokovec, Slovakia

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 34st International Symposium on Mathematical Foundations of Computer Science (MFCS)
• Publication Date: Aug 1, 2009
• Deposit Date: Dec 8, 2011
• Publicly Available Date: Sep 16, 2014
• Print ISSN: 0302-9743
• Pages: 403-414
• Series Title: Lecture notes in computer science
• Series Number: 5734
• Series ISSN: 0302-9743,1611-3349
• Book Title: Mathematical foundations of computer science 2009 34th international symposium, MFCS 2009, Novy Smokovec, High Tatras, Slovakia, August 24-28, 2009 : proceedings.
• DOI: https://doi.org/10.1007/978-3-642-03816-7_35
• Keywords: Longest path problem, Interval graphs, Polynomial algorithm, Complexity, Dynamic programming.
• Public URL: https://durham-repository.worktribe.com/output/1157550
• Additional Information: Proceedings published as: Mathematical Foundations of Computer Science 2009, 34th International Symposium, MFCS 2009, Novy Smokovec, High Tatras, Slovakia, August 24-28, 2009. Symposium url: http://www.mfcs.sk/mfcs2009/