Publication details for Dr George MertziosIoannidou, K., Mertzios, G.B. & Nikolopoulos, S.D. (2009), The longest path problem is polynomial on interval graphs, in Rastislav Královic and Damian Niwinski eds, Lecture Notes in Computer Science (LNCS) 5734: 34st International Symposium on Mathematical Foundations of Computer Science (MFCS). Novy Smokovec, Slovakia, Springer, Novy Smokovec, 403-414.
- Publication type: Conference Paper
- ISSN/ISBN: 0302-9743, 1611-3349, 9783642038150
- DOI: 10.1007/978-3-642-03816-7_35
- Keywords: Longest path problem, Interval graphs, Polynomial algorithm, Complexity, Dynamic programming.
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
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 , 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.
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/