Virtual and Consistent Hyperbolic Tree: A New Structure for Distributed Database Management

Abstract

Abstract. This paper describes a new scalable, reliable and consistent structure for implementing a distributed database system. This structure is based on the hyperbolic geometry and we call it a Virtual and Consistent Hyperbolic tree (VCH-tree). This structure is intended for supporting queries over possibly large spatial datasets distributed over interconnected servers. The VCH-tree is comparable to the well-known R-tree structure, but it uses the hyperbolic geometry properties of the Poincaré disk model. It uses a distributed balanced Q-degree spatial tree that scales with data objects' insertions into potentially any number of storage servers through virtual hyperbolic coordinates. A user application manipulates the structure from a client node. The client can connect to the system through one of the database servers that is already in the VCH-tree. Messages are then routed towards the proper server by a greedy algorithm which is using the virtual hyperbolic coordinates attributed to each server. We have performed simulations to assess the efficiency and reliability of the VCH-tree. Results show that our VCHtree is consistent and has expected performances given the scalability and flexibility it provides to distributed database applications.

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“…Typically, when the η node tries to reach the µ node, it calculates the distance between its correspondent µ and each of its own neighbours, and it selects, in fine, the neighbours v having the shortest hyperbolic distance with the destination node µ. Mathematically, the distance between any two points u and v, taken in the hyperbolic space H, is determined by equation 4.2.1 [7]:…”

“…In the Poincaré disk model, the hyperbolic tree is scalable [7]. Figure 3 illustrates the object storage process in a DHT-based system.…”

“…It is a simple and scalable faulttolerant data processing environment that allows its users to process massive distributed and large-scale data to extract new knowledge. Recent studies have shown the limitations of MapReduce [5] and have proposed DHTs [6], [7] as solutions for incidents that could impact the digital world. As part of this work, we present our architecture inspired by [6] to which we will add some properties of digital imaging [8] for better data management and we will end with an intuitive comparison of our model with existing models.…”

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“…Step 7: In the Poincaré disk model, the hyperbolic tree is scalable [7]. Figure 3 illustrates the object storage process in a DHT-based system.…”