New Results on Server Problems

Abstract

In the k-server problem, we must choose how k mobile servers will serve each of a sequence of requests, making our decisions in an online manner. We exhibit an optimal deterministic online strategy 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, we also provide an optimal deterministic algorithm. We prove the nonexistence of competitive algorithms for the asymmetric two-server problem, and of memoryless algorithms for the weighted-cache problem. We give a fast algorithm for offline computing of an optimal schedule, and show that finding an optimal offline schedule is at least as hard as the assignment problem. 1 Introduction The k-server problem can be stated as follows. We are given a metric space M , and k servers which move among the points of M , each occupying one point of M . Repeatedly, a request (a point x 2 M) appears. To serve x, each server moves some distance, possibly..