Optimal Data Placement on Networks With Constant Number of Clients

TL;DR

This paper presents optimal algorithms for data and page placement in networks with a fixed number of clients, achieving optimal or near-optimal solutions without assumptions on network topology.

Contribution

Introduces the first non-trivial optimal algorithms for data placement problems in non-metric networks with a constant number of clients, handling uniform and non-uniform object sizes.

Findings

Optimal solutions for uniform object lengths

Near-optimal solutions with small violations for non-uniform objects

No assumptions on network topology, broad applicability

Abstract

We introduce optimal algorithms for the problems of data placement (DP) and page placement (PP) in networks with a constant number of clients each of which has limited storage availability and issues requests for data objects. The objective for both problems is to efficiently utilize each client's storage (deciding where to place replicas of objects) so that the total incurred access and installation cost over all clients is minimized. In the PP problem an extra constraint on the maximum number of clients served by a single client must be satisfied. Our algorithms solve both problems optimally when all objects have uniform lengths. When objects lengths are non-uniform we also find the optimal solution, albeit a small, asymptotically tight violation of each client's storage size by $\epsilon$lmax where lmax is the maximum length of the objects and $\epsilon$ some arbitrarily small positive constant. We make no assumption on the underlying topology of the network (metric, ultrametric etc.), thus obtaining the first non-trivial results for non-metric data placement problems.