Competitive access time via dynamic storage rearrangement

The problem of storing items in some warehouse where a server has to visit items over time, with the goal of minimizing the total distance traversed by the server, is modeled. A study of the dynamic version of the problem is made, where the robot may rearrange the warehouse to deal efficiently with future events. No statistical assumptions are required on the access pattern, and competitive algorithms are given that rearrange the warehouse over time to deal efficiently with the true access patterns. Non-trivial upper bounds are given for the general problem, along with some interesting lower bounds. In addition, realistic data access patterns on disk storage are modeled by considering two practically significant 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 greatly improved competitive ratios are given.