Provably Good and Practical Strategies for Non-uniform Data Management in Networks

Abstract

This paper deals with the on-line allocation of shared data objects to the local memory modules of the nodes in a network. We assume that the data is organized in indivisible objects such as files, pages, or global variables. The data objects can be replicated and discarded over time in order to minimize the communication load for read and write accesses done by the nodes in the network. Non-uniform data management is characterized by a different communication load for accesses to small pieces of the data objects and migrations of whole data objects.

We introduce on-line algorithms that minimize the congestion, i.e., the maximum communication load over all links. Our algorithms are evaluated in a competitive analysis comparing the congestion produced by an on-line algorithm with the congestion produced by an optimal off-line algorithm.We present the first deterministic and distributed algorithm that achieves a constant competitive ratio on trees. Our algorithm minimizes not only the congestion but minimizes simultaneously the load on each individual edge up to a optimal factor of 3.

Algorithms for trees are of special interest as they can be used as a subroutine in algorithms for other networks. For example, using our tree algorithm as a subroutine in the recently introduced “access tree strategy” yields an algorithm that is O(d · logn)-competitive for d-dimensional meshes with n nodes. This competitive ratio is known to be optimal for meshes of constant dimension.

F. Meyer auf der Heide and M. Westermann are supported in part by DFG-Sonderforschungsbereich 376 and EU ESPRIT Long Term Research Project 20244 (ALCOM-IT). B. Vöcking is supported by a grant of the “Gemeinsames Hochschulsonderprogramm III von Bund und Ländern” through the DAAD.