The idea of generalized indices is one of the success stories of database systems research. It has found its way to implementation in common database systems. GiST (Generalized Search Tree) and SP-GiST (Space-Partitioned Generalized Search Tree) are two widely-used generalized indices that are typically used for multidimensional data, e.g., to index spatial or spatio-temporal data. Currently, the generalized indices GiST and SP-GiST represent one database object using one index entry, e.g., a scalar value or abounding box for each spatial or spatio-temporal object. However, when dealing with complex objects, e.g., moving object trajectories, a single entry per object is inadequate for creating efficient indices. Previous research has highlighted that splitting trajectories into multiple sub-trajectories or bounding boxes prior to indexing can enhance query performance as it leads to a higher index filter. In this paper, we introduce MGiST and MSP-GiST, the multi-entry generalized search tree counterparts of GiST and SP-GiST, respectively, that are designed to enable the partitioning of objects into multiple entries during insertion. The methods for decomposing a complex object into multiple sub-objects differ from one data type to another, and may depend on some domain-specific parameters. Thus, MGiST and MSP-GiST are designed to allow for pluggable modules that aid in optimizing the split of an object into multiple sub-objects. We demonstrate the usefulness of MGiST and MSP-GiST using a trajectory indexing scenario, where we realize several trajectory indexes using MGiST and MSP-GiST and instantiate these search trees with trajectory-specific splitting algorithms. We create and test the performance of several multi-entry versions of widely-used spatial index structures, e.g., R-Tree, Quad-Tree, and KD-Tree. We conduct evaluations using both synthetic and real-world data, and observe up to an order of magnitude enhancement in performance of point, range, and nearest neighbor queries.

Various applications process geospatial trajectories of moving objects, such as cars, ships and robots. There is thus a need for a common conceptual framework to model and manage these objects, as well as to enable data interoperability across tools. The International Organization for Standardization ISO® has responded to this need and created the standard ISO 19141- Schema for moving features. Among its types, it defines a schema for rigid temporal geometries, which represent the movement of spatial objects translating and rotating over time, while preserving a fixed shape. Despite the abundance of these objects in real-world, there exists no reference implementation of this type of data in a common system, which causes them to usually be represented as temporal points without taking into account their spatial extents and shapes. In this paper, we aim to provide an implementation of rigid temporal geometries into MobilityDB, an open-source moving object database, that extends PostgreSQL and PostGIS. We provide a data model for rigid temporal geometries and propose efficient algorithms for the operations defined in ISO 19141. A use case on real AIS ship trajectories is illustrated to validate the proposed implementation. A synthetic data generator for temporal geometries is also proposed. Finally, we review the standard from an implementation point of view and provide insights on possible improvements.