A Randomized Algorithm for Two Servers in Cross Polytope Spaces

It has been a long-standing open problem to determine the exact randomized competitiveness of the 2-server problem, that is, the minimum competitiveness of any randomized online algorithm for the 2-server problem. For deterministic algorithms the best competitive ratio that can be obtained is 2 and no randomized algorithm is known that improves this ratio for general spaces. For the line, Bartal et al. [2] give a 155 78 competitive algorithm, but their algorithm is specific to the geometry of the line. We consider here the 2-server problem over Cross Polytope Spaces M2,4. We obtain an algorithm with competitive ratio of 19 12 , and show that this ratio is best possible. This algorithm gives the second non-trivial example of metric spaces with better than 2 competitive ratio. The algorithm uses a design technique called the knowledge state technique – a method not specific to M2,4.