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A fully peer-to-peer (P2P) virtual environment (VE) represents a unique challenge in the realm of extreme distributed systems. Resource scalability and system resiliency, hallmark requirements of the P2P principle, are further complicated with the need for secure and responsive game-play amongst the millions of players in a P2P-VE. Inter-peer communications need to be almost real-time in nature, to facilitate a smooth, immersive experience and provide consistency within the virtual world. Players will not tolerate slow connections and players who cheat by modifying or delaying inter-peer updates. 3D Voronoi diagrams are a natural extension to traditional 2D varieties and they serve as the foundation for our proposed approach. We augment our 3D-VD platform with a novel concept: the usual spatial coordinates for the 3rd dimension is substituted with a non-spatial metric. Instead of taking the Z-axis to …