Approximation algorithms for data placement on parallel disks

Abstract

We study an optimization problem that arises in the context of data placement in a multimedia storage system. We are given a collection of M multimedia objects (data objects) that need to be assigned to a storage system consisting of N disks d 1 , d 2 …, d N . We are also given sets U 1 , U 2 ,…, U M such that U i is the set of clients seeking the i th 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 to 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 . We show that an algorithm developed by Shachnai and Tamir [2000a] for data placement achieves the best possible absolute bound regarding the number of clients that can always be satisfied. We also show how to implement the algorithm so that it has a running time of O (( N + M ) log( N + M )). In addition, we design a polynomial-time approximation scheme, solving an open problem posed in the same paper.