Historical spatio-temporal aggregation

Abstract

Spatio-temporal databases store information about the positions of individual objects over time. However, in many applications such as traffic supervision or mobile communication systems, only summarized data, like the number of cars in an area for a specific period, or phone-calls serviced by a cell each day, is required. Although this information can be obtained from operational databases, its computation is expensive, rendering online processing inapplicable. In this paper, we present specialized methods, which integrate spatio-temporal indexing with preaggregation. The methods support dynamic spatio-temporal dimensions for the efficient processing of historical aggregate queries without a-priori knowledge of grouping hierarchies. The superiority of the proposed techniques over existing methods is demonstrated through a comprehensive probabilistic analysis and an extensive experimental evaluation.

Statistical Regular Pavings to Analyze Massive Data of Aircraft Trajectories

“…Other tree-based data structures are used in [6] and [7] to analyze moving objects, with the common aim of answering range queries efficiently, which typically involves getting the number of points (planes) that are contained in some query box (location). Variations and extensions of wellknown R trees (R for rectangle) for spatial access and queries are used in [6].…”

“…Note that the aggregated SRP object at an instant of time t has to be a {0, 1}-valued structure to remain collision free, for if the value at a leaf box or cell is more than one at an instant of time, then it means that a collision has happened there. One of the main objectives in [7] is the development of algorithms that maintain the median of a set of moving points for both the on-line (i.e., our n 1:m:... -sensing setting) and off-line setting (i.e., our n-presensed or n 1:m -presensed settings). The algorithms in [7] use kinetic kd trees on sets of moving objects for query tasks.…”

“…One of the main objectives in [7] is the development of algorithms that maintain the median of a set of moving points for both the on-line (i.e., our n 1:m:... -sensing setting) and off-line setting (i.e., our n-presensed or n 1:m -presensed settings). The algorithms in [7] use kinetic kd trees on sets of moving objects for query tasks. Typically, a kd-tree is built by splitting the data at the coordinate-specific median into two subsets where splits are done by alternating at the coordinates.…”

“…Two variants of kd-trees are proposed: a δ-pseudo kd-tree (which turns out to be an almost balanced tree) that allows for efficient insertion and deletion, and a δ-overlapping kd-tree (a perfectly balanced tree) where the bounding boxes of two children are allowed to overlap. Similar to the R-trees in [6], the kd-trees in [7] have nodes that already contain summarized information and are essentially different from our basic SRP objects that are specific to a flight instance.…”

“…Finally, we would like to emphasize that our SRP trees are uniquely suited to perform efficient arithmetic operations, especially on a set of aggregated SRP objects for, say, cotrajectory pattern analyses, especially in conjunction with local weather data. We think that the data structures in [3], [6] and [7] can be used in complementary ways with SRPs, for which the real strength lies in performing arithmetic operations over the space of trajectories and cotrajectories, to comprehensively deal with downstream decision problems using our SRP arithmetics bolstered by interactive visualization in [3] as well as fast querying and coarse aggregation in [6] and [7]. Denote the space of such intervals as IR.…”