Approximation Algorithms for Data Management in Networks

This paper deals with static data management in computer systems connected by networks. A basic functionality in these systems is the interactive use of shared data objects that can be accessed from each computer in the system. Examples for these objects are files in distributed file systems, cache lines in virtual shared memory systems, or pages in the WWW. In the static scenario we are given read and write request frequencies for each computer-object pair. The goal is to calculate a placement of the objects to the memory modules, possibly with redundancy, such that a given cost function is minimized. With the widespread use of commercial networks, as, e.g., the Internet, it is more and more important to consider commercial factors within data management strategies. The goal in previous work was to utilize the available resources, especially the bandwidth, as best as possible. We present data management strategies for a model in which commercial cost instead of the communication cost is minimized, i.e., we are given a metric communication cost function and a storage cost function. We introduce new deterministic algorithms for the static data management problem on trees and arbitrary networks. Our algorithms aim to minimize the total cost. Note that this problem is MaxSNP-hard on arbitrary networks. Our main result is a combinatorial algorithm that calculates a constant factor approximation for arbitrary networks in polynomial time. Further, we present a dynamic programming algorithm for trees that calculates an optimal placement of all objects in X on a tree T = (V, E) in time O(|X| · |V| · diam(T) · log(deg(T))).