Time via Dynamic

We model the problem of storing items in some warehouse (modeled as an undirected graph) where a server has to visit items over time, with the goal of minimizing the total distance traversed by the server. Special cases of this problem include the management of a real industrial stacker crane warehouse G], automatic robot run warehouses Ho], disk track optimization to minimize access time GS, P, W, YW], managing two dimensional memory (bubble memory and mass storage systems) KMW, W, YW], doubly linked list management , and the process migration problem. The static version of this problem assumes some known probability distribution on the access patterns. The study of special cases of this static version was rst considered by Hardy, Littlewood and PP olya in 1932 HLP]. In this work we initiate the study of the dynamic version of the problem, where the robot may rearrange the warehouse to deal eeciently with future events. We require no statistical assumptions on the access pattern , and give competitive algorithms that rearrange the warehouse over time to deal eeciently with the true access patterns. We give non-trivial upper bounds for the general problem, along with some interesting lower bounds. In addition, we model realistic data access patterns on disk storage by considering two practically sig-niicant scenarios: access to some database via dynamically changing alternative indices and access patterns derived from root to leaf traversals of some (unknown) tree structure. In both cases we give greatly improved competitive ratios.