A New Spatial Database Management System Using an Hyperbolic Tree

Spatial information processing has been a focus of research in the past decade. In spatial databases, data are associated with spatial coordinates and extents, and are retrieved based on spatial proximity. A formidable number of spatial indexes have been proposed to facilitate spatial data retrieval. In this paper, we propose a new scalable, reliable and consistent architecture for spatial database indexing based on hyperbolic topology. This structure uses a strategy that enables to avoid such an exhaustive search that is based on the use of a centralized index. Our architecture is comparable to the well-known Rtree structure, but uses the hyperbolic geometry properties with specific model called “Poincaré disk model”. It uses a distributed balanced Q-degree spatial tree that scales with spatial data objects insertions into potentially any number of storage servers through virtual hyperbolic coordinates taken in hyperbolic space. In other words, we propose a new model based on structured Distributed Hash Table (DHT) in which a user/application of each server is considered as a client node. Thus, a database server can connect to the system through a random database server that already addresses the tree with a free address given by one other database server of the system. Database servers addresses are associated with virtual hyperbolic coordinates computed by the system. In this paper, we consider a 3-regular Hyperbolic-tree in the hyperbolic plane; so, except for the root of this tree, others servers have in the best cases two addresses to give a new one (server’s father uses one address). In our work, we perform simulations and we analyze the practicability and reliability compared with other DHT, such as Chord, Pastry, Kademlia used in other spatial databases. The results show that our spatial architecture based on a hyperbolic tree is viable, consistent and has acceptable performances given the scalability and flexibility it could provide to distributed database applications. Keywords–Spatial Database; Management; Hyperbolic-Tree; Query; Storage.