# MobilityDB: A PostgreSQL extension for mobility data management

We will be presenting MobilityDB, a PostgreSQL extension that extends the type system of PostgreSQL and PostGIS with abstract data types for representing moving object data. These types can represent the evolution on time of values of some element type, called the base type of the temporal type. For instance, temporal integers may be used to represent the evolution on time of the number of employees of a department. In this case, the data type is “temporal integer” and “integer” is the base type. Similarly, a temporal float may be used to represent the evolution on time of the temperature of a room. As another example, a temporal point may be used to represent the evolution on time of the location of a car, as reported by GPS devices. Temporal types are useful because representing values that evolve in time is essential in many applications, for example in mobility applications.

The temporal types in MobilityDB are based on the bool, int, float, and text base types provided by PostgreSQL, and on the geometry and geography base types provided by PostGIS (restricted to 2D or 3D points). MobilityDB follows the ongoing OGC standards on Moving Features (http://www.opengeospatial.org/standards/movingfeatures), and in particular the OGC Moving Features Access, which specifies operations that can be applied to time-varying geometries.

A rich set of functions and operators is available to perform various operations on temporal types. In general there are three classes:

- Lifed functions and operators: the operators on the base types (such as arithmetic operators and for integers and floats, spatial relationships and distance for geometries) are intuitively generalized when the values evolve in time. Spatiotemporal functions in MobilityDB generalize spatial functions provided by PostGIS for both "geometry" and "geography" types, for instance the "ST_Intersection". Basically, MobilityDB takes care of the temporal aspects and delegates the spatial processing to PostGIS.
- Temporal functions and operators: they process the temporal dimension of the value which can be an instant, a range, an array of instant, or an array of ranges. Examples are the atperiods function that restricts a temporal type to a given array of time ranges, and the duration function that extracts the definition time of a value.
- Spatiotemporal functions and operators: all remaining functions fall into this category. Examples are speed(tgeompoint/tgeogpoint), azimuth(tgeompoint/tgeogpoint), maxValue(tfloat/tint), twAvg(tfloat) a time weighted average, etc.

Both GiST and SP-GiST have been extended to support the temporal types. The GiST index implements an R-tree for temporal alphanumeric types and a TB-tree for temporal point types. The SP-GiST index implements a Quad-tree for temporal alphanumeric types and an Oct-tree for temporal point types. The approach used for developing SP-GIST indexes for MobilityDB allowed us to add SP-GIST indexes for 2-dimensional, 3-dimensional and n-dimensional geometries in PostGIS.

Two types of numeric aggregate functions are available. In addition to the traditional functions min, max, count, sum, and avg, there are window (also known as cumulative) versions of them. Given a time interval w, the window aggregate functions compute the value of the function at an instant t by considering the values during the interval [t − w, t]. In contrast to standard aggregation, temporal aggregation may return a result which is of a bigger size than the input. For this reason, the temporal aggregate functions have been extremely optimized in order to perform efficiently.

MobilityDB has a preliminary implementation of the statistic collector functions and the selectivity functions for the temporal types.

In terms of size, the extension is made of 67k lines of C code, 19k lines of SQL code, 67k lines of SQL unit tests. It defines 40 types, 2300 functions, and 1350 operators.

The talk will illustrate the spatiotemporal concepts and the data model of the temporal types. It will briefly describe the components of MobilityDB: indexing, aggregations, functions and operators, and the SQL interface. Query examples and uses cases will be illustrated allover the talk. The current status of MobilityDB and the planned development will also be presented.

The talk shall be given by: - Esteban Zimányi: Professor and Director of the Department of Computer and Decision Engineering of the Universite Libre de Bruxelles. - Mahmoud SAKR: Postdoc researcher in the Universite Libre de Bruxelles.