Virtual and consistent hyperbolic tree: A new structure for distributed database management

Abstract

We describe a new structure called Virtual and Consistent Hyperbolic tree (VCH-tree) for implementing a distributed database system. This structure is based on the hyperbolic geometry and can support queries over large spatial data sets, distributed over interconnected servers. The VCH-tree is comparable to the well-known R-tree structure, but it leverages the hyperbolic geometry properties of the Poincaré disk model. It maintains a balanced Q-degree spatial tree that scales with insertions of data objects into a large number of servers, reachable through hyperbolic coordinates. A user application manipulates the structure from a client node. The client can connect to the system through one of the servers that is already in the VCH-tree. Messages are then routed towards the proper server by a greedy algorithm which uses the hyperbolic coordinates attributed to each server. We have performed simulations to assess the efficiency and reliability of the VCH-tree. Results show that our VCH-tree exhibits expected performances for being used by distributed database applications.