NDLI: The Longest Path Problem has a Polynomial Solution on Interval Graphs

Content Provider	Springer Nature Link
Author	Ioannidou, Kyriaki Mertzios, George B. Nikolopoulos, Stavros D.
Copyright Year	2010
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.
Starting Page	320
Ending Page	341
Page Count	22
File Format	PDF
ISSN	01784617
Journal	Algorithmica
Volume Number	61
Issue Number	2
e-ISSN	14320541
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-05-12
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Longest path problem Interval graphs Polynomial algorithm Complexity Dynamic programming Data Structures, Cryptology and Information Theory Mathematics of Computing Theory of Computation Computer Systems Organization and Communication Networks Algorithms Algorithm Analysis and Problem Complexity
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computer Science Applications

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