A Competitive Algorithm for the General 2-Server Problem

We consider the general on-line two server problem in which at each step both servers receive a request, which is a point in a metric space. One of the servers has to be moved to its request. The special case where the requests are points on the real line is known as the CNN-problem. It has been a well-known open question if an algorithm with a constant competitive ratio exists for this problem. We answer this question in the affirmative sense by providing the first constant competitive algorithm for the general two-server problem on any metric space.