Highest order voronoi diagram for region-based spatial query processing

Abstract

A spatial database is a database that is optimized for storing and querying data that represents objects as points, lines or polygons. A spatial query is a mechanism for retrieving objects stored in the database and consists of a specific question with certain parameters in a map. In general, a spatial query is intended to retrieve the objects either as a set of points of interests or a region for the answer. To get the answer, the query can be processed in two different ways: point-to-point calculation or region-based calculation. In point-to-point calculation, the query can be solved by choosing appropriate objects on the map that can be used to answer the query. In region-based calculation, the query can be solved by constructing the region that contains the correct objects that will answer the query. Region-based calculation has one major advantage over point-to-point calculation: this method does not need to check each object one-by-one; hence this method will not suffer from performance degradation where there is a high number of objects. A region-based calculation method that is commonly used to solve spatial queries is the Voronoi diagram. This method divides the map into smaller spaces based on the nearest distance to an object. A Voronoi diagram can mimic human visual intuition, where humans can easily identify whether an object is located inside or outside a closed shape. Even though a Voronoi diagram has been applied widely for various spatial query types, this diagram has some problems, which are: (1) Most queries use a Voronoi diagram only to prune the map to reduce the objects verification time, (2) The region to answer a spatial query cannot be retrieved directly from a complete Voronoi diagram even though the region for a spatial query is part of a Voronoi diagram. Each type of query needs a specific method in order to generate the region. Therefore this thesis will present a new variation of the Voronoi diagram named highest order Voronoi diagram (HSVD) that can be used directly to identify the region for various types of spatial queries. To show the flexibility of this structure, we applied it to commonly known nearest neighbours and reverse nearest neighbours with their queries variations. We also applied this structure to answer polychromatic queries and extend this method for hierarchical queries. Our analysis shows that the HSVD structure is very flexible and can adapt to various types of spatial queries without having to rebuild the current structure to answer variations in the queries.