  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(n^2 (n+m)), where n is the number of the vertices and m is the
number of edges.
