Emergent Mind
A greedy approximation algorithm for the longest path problem in undirected graphs
(1209.2503)
Published Sep 12, 2012
in
cs.DS
Abstract
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general graphs, since it includes the Hamiltonian path problem as a special case [3]. Motivated by finding a simple, quick algorithm for finding long paths in large graphs, in this paper we show a greedy algorithm with a time complexity of O(n2 (n+m)), where n is the number of the vertices and m is the number of edges.
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