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The longest path problem is polynomial on interval graphs

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

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Authors

K. Ioannidou

S.D. Nikolopoulos



Contributors

Královič Rastislav
Editor

Niwinski Damian
Editor

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). The longest path problem is polynomial on interval graphs. In K. Rastislav, & N. Damian (Eds.), Mathematical foundations of computer science 2009 34th international symposium, MFCS 2009, Novy Smokovec, High Tatras, Slovakia, August 24-28, 2009 : proceedings (403-414). https://doi.org/10.1007/978-3-642-03816-7_35

Conference Name 34st International Symposium on Mathematical Foundations of Computer Science (MFCS)
Conference Location Novy Smokovec, Slovakia
Publication Date Aug 1, 2009
Deposit Date Dec 8, 2011
Publicly Available Date Mar 28, 2024
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/

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