Maintaining interactivity is one of the key challenges in distributed virtual environments (DVE) due to the large, heterogeneous Internet latency and the fact that clients in a DVE are usually geographically separated. Previous work in this area have dealt with optimizing interactivity performance given limited server resource. In this paper, we consider a new problem, termed the performance-constrained server provisioning, whose goal is to minimize the resource needed to achieve a pre-determined level of Quality of Service (QoS). We identify and formulate two variants of this new problem and show that they are both NP-hard via reductions to the set covering problem. We also propose several computationally efficient approximation algorithms for solving the problem. Via extensive simulation study, we show that the newly proposed algorithms that take into account inter-server dependencies significantly outperform the well-known set covering algorithm for both problem variants.
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