Publication details for Dr George MertziosIoannidou, K., Mertzios, G.B. & Nikolopoulos, S.D. (2011). The longest path problem has a polynomial solution on interval graphs. Algorithmica 61(2): 320-341.
- Publication type: Journal Article
- ISSN/ISBN: 0178-4617, 1432-0541
- DOI: 10.1007/s00453-010-9411-3
- 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 (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.