New Ressults on Server Problems

In the k-server problem, one must choose how k mobile servers will serve each of a sequence of requests, making decisions in an online manner. An optimal deterministic online strategy is exhibited when the requests fall on the real line. For the weighted-cache problem, in which the cost of moving to x from any other point is $w( x )$, the weight of x, an optimal deterministic algorithm is also provided. The nonexistence of competitive algorithms for the asymmetric two-server problem and of memoryless algorithms for the weighted-cache problem is proved. A fast algorithm for oflline computing of an optimal schedule is given, and it is shown that finding an optimal offline schedule is at least as hard as the assignment problem.