2012/09/12 by Pongrácz, Lajos L.
#Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1209.2503
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.