Minimizing the Maximum Flow Time in the Online-TSP on the Real Line

In the online traveling salesman problem (OlTsp) requests for visits to cities arrive online while the salesman is traveling. The Fmax-OlTsp has as objective to minimize the maximum flow time, which 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 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 where there are yet unserved requests. Our main result is an 8-competitive algorithm against the non-abusive adversary.