The longest path problem has a polynomial solution on interval graphs

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

doi:10.1007/s00453-010-9411-3

The longest path problem has a polynomial solution on interval graphs

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

Authors

K. Ioannidou

Dr George Mertzios george.mertzios@durham.ac.uk
Associate Professor

S.D. Nikolopoulos

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.