Algorithms for the On-Line Travelling Salesman.

摘要

In this paper the problem of efficiently serving a sequence of requests presented in an on-line fashion located at points of a metric space is considered. The authors call this problem the On-Line Travelling Salesman Problem (OLTSP). It has a variety of relevant applications in logistics and robotics. The authors consider two versions of the problem. In the first one the server is not required to return to the departure point after all presented requests have been served. For this problem the authors derive a lower bound on the competitive ratio of 2 on the real line. Besides, a 2.5-competitive algorithm for a wide class of metric spaces, and a 7/3-competitive algorithm for the real line are provided. For the other version of the problem, in which returning to the departure point is required, the authors present an optimal 2-competitive algorithm for the above mentioned general class of metric spaces. If in this case the metric space is the real line the authors present a 1.75-competitive algorithm that compares with an approximately 1.64 lower bound.