An efficient parallel algorithm for the longest path problem in meshes

Authors:
Fatemeh Keshavarz-Kohjerdi;Alireza Bagheri
Affiliations:
Department of Computer Engineering & IT, Amirkabir University of Technology, Tehran, Iran;Department of Computer Engineering & IT, Amirkabir University of Technology, Tehran, Iran
Venue:
The Journal of Supercomputing
Year:
2013

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Abstract

The longest path problem is the problem of finding a simple path with the maximum number of vertices in a given graph, and so far it has been solved polynomially only for a few classes of graphs. This problem generalizes the well-known Hamiltonian path problem, hence it is NP-hard in general graphs. In this paper, first we give a sequential linear-time algorithm for the longest path problem in meshes. Then based on this algorithm, we present a constant-time parallel algorithm for the problem, which can be run on every parallel machine.