A linear-time algorithm for the longest path problem in rectangular grid graphs

Authors:
Fatemeh Keshavarz-Kohjerdi;Alireza Bagheri;Asghar Asgharian-Sardroud
Affiliations:
Department of Computer Engineering, Islamic Azad University, North Tehran Branch, Tehran, Iran;Department of Computer Engineering & IT, Amirkabir University of Technology, Tehran, Iran;Department of Computer Engineering & IT, Amirkabir University of Technology, Tehran, Iran
Venue:
Discrete Applied Mathematics
Year:
2012

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Abstract

The longest path problem is a well-known NP-hard problem and so far it has been solved polynomially only for a few classes of graphs. In this paper, we give a linear-time algorithm for finding a longest path between any two given vertices in a rectangular grid graph.