Approximation algorithms for data placement on parallel disks

We study an optimization problem that arises in the context of data placement in multimedia storage systems. We are given a collection of M multimedia data objects that need to be assigned to a storage system consisting of N disks d₁, d₂ …, d_N. We are also given sets U₁, U₂, …, U_M such that U_i is the set of clients requesting the ith data object. Each disk d_j is characterized by two parameters, namely, its storage capacity C_j which indicates the maximum number of data objects that may be assigned to it, and a load capacity L_j which indicates the maximum number of clients that it can serve. The goal is to find a placement of data objects on disks and an assignment of clients to disks so as to maximize the total number of clients served, subject to the capacity constraints of the storage system. We study this data placement problem for two natural classes of storage systems, namely, homogeneous and uniform ratio. Our first main result is a tight upper and lower bound on the number of items that can always be packed for any input instance to homogeneous as well as uniform ratio storage systems. We show that an algorithm given in [11] for data placement, achieves this bound. Our second main result is a polynomial time approximation scheme for the data placement problem in homogeneous and uniform ratio storage systems, answering an open question of [11]. Finally, we also study the problem from an empirical perspective.