On the LP Relaxation of the Asymmetric Traveling Salesman Path Problem

This is a comment on the article “An O(logn) Approximation Ratio for the Asymmetric Traveling Salesman Path Problem” by C. Chekuri and M. Pál, Theory of Computing 3 (2007), 197–209. We observe that the LP relaxation for the Asymmetric Traveling Salesman Path Problem suggested in Section 5 of that paper is not accurate, and state a corrected linear relaxation for the problem. The inaccuracy occurs in the statement of an open problem and does not affect the validity of any of the results in the Chekuri–Pál paper. ACM Classification: F.2.2, G.2.2 AMS Classification: 68W25, 68R10, 90C59