The longest path problem has a polynomial solution 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 (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.

Citation

Ioannidou, K., Mertzios, G., & Nikolopoulos, S. (2011). The longest path problem has a polynomial solution on interval graphs. Algorithmica, 61(2), 320-341. https://doi.org/10.1007/s00453-010-9411-3

• Journal Article Type: Article
• Publication Date: Oct 1, 2011
• Deposit Date: Dec 8, 2011
• Publicly Available Date: Jan 10, 2012
• Journal: Algorithmica
• Print ISSN: 0178-4617
• Electronic ISSN: 1432-0541
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 61
• Issue: 2
• Pages: 320-341
• DOI: https://doi.org/10.1007/s00453-010-9411-3
• Keywords: Longest path problem, Interval graphs, Polynomial algorithm, Complexity, Dynamic programming.
• Public URL: https://durham-repository.worktribe.com/output/1533458