Non-abusiveness helps: An O(1)-competitive algorithm for minimizing the maximum flow time in the online traveling salesman problem

In the online traveling salesman problem OlTsp requests for visits to cities arrive online while the salesman is traveling. We study the Fmax-OLTsp where the objective is to minimize the maximum flow time. This objective is particularly interesting for applications. Unfortunately, there can be no competitive algorithm, neither deterministic nor randomized. Hence, competitive analysis fails to distinguish online algorithms. Not even resource augmentation which is helpful in scheduling works as a remedy. This unsatisfactory situation motivates the search for alternative analysis methods. We introduce a natural restriction on the adversary for the Fmax-OlTsp on the real line. A non-abusive adversary may only move in a direction if there are yet unserved requests on this side. Our main result is an algorithm which achieves a constant competitive ratio against the nonabusive adversary. © Springer-Verlag Berlin Heidelberg 2002.