  Starting with M(a), an n X n asymmetric cost matrix, Jonker and Volgenannt
transformed it into a 2n X 2n symmetric cost matrix, M(s)where M(s) has unusual
properties. One such property is that an optimal tour in M(s) yields an optimal
tour in M(a). Modifying M(s), we apply the modified Floyd-Warshall algorithm to
M(s). Due to the structure of M(s), we hopefully)can always obtain an optimal
tour in M(a) in polynomial time.If theorem 1 in this paper is valid, since the
asymmetric traveling salesman problem is NP-hard, P would equal NP.
