Multidimensional range queries on hierarchical Voronoi overlays

• We define a multidimensional range query support for distributed systems.
• We exploit Voronoi Tessellations to build the distributed overlay.
• We define a hierarchical overlay.
• The paper includes complexity analysis for the operations defined on the overlay.
• The paper presents a set of simulations performed on synthetic data and on a real data set.

The definition of a support for multi-attribute range queries is mandatory for highly distributed systems. Even if several solutions have been proposed in the last decade, most of them do not meet the requirements of recent platforms, like IoT or smart cities. The paper presents an approach that builds a multidimensional Voronoi graph by exploiting the attributes of the objects published by a node. Our solution overcomes the curse of dimensionality issue affecting Voronoi Tessellations in high dimensional spaces by defining a Voronoi hierarchy. The paper formally defines the structure, analysis the complexity of the operations and presents experimental results.