About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
Information Processing Letters
Paper
A tight lower bound for the train reversal problem
Abstract
In a 1987 Scientific American Computer Recreations article, A.K. Dewdney posed the problem of reversing an n-car train on a track with a one-car spur using the minimum amount of work. In that article, Dewdney indicated an algorithm for reversing the train that uses O(n3) work. Shortly thereafter, Amato, Blum, Irani and Rubinfeld (Reversing Trains: A Turn of the Century Sorting Problem, J. Algorithms, Vol. 10, 1989, pp. 413-428) discovered a simple recursive algorithm that requires O(n2logn) work to reverse a train. In this paper, we prove that Amato et al.'s algorithm is optimal up to a constant factor, i.e., we prove that any algorithm for reversing an n-car train in the Dewdney model requires Ω(n2log n) work. © 1990.