1. Spatio-Temporal Databases

2. Introduction Spatiotemporal Databases: manage spatial data whose geometry changes over time Geometry: position and/or extent Global change data: climate or land cover changes Transportation: cars, airplanes Animated movies/video DBs

3. Spatio-temporal Queries Historical Queries: Store the past the history of a spatio-temporal evolution. R-tree, PPR-tree “Future” Queries: Find the future positions of moving objects. Indexing?

4. Indexing moving objects Database stores the current location of each object and the velocity vector. Example: cars moving in a highway system. GPS can provide position/velocity

5. Moving Objects: Queries Range Queries NN queries Aggregation queries : no good solutions so far Q

6. Moving Objects:Representation Consider the 1-d case (objects moving on a line) Storing the locations of moving objects is a challenge: Update the database with the new locations Use a function of time f(t) to store a location Update overhead is reduced; update the database only when velocity changes

7. Space-time Trajectories are plotted as lines in the time-location space (y, t); p(t) = vt+a (t) time o o o o 1 2 3 4 trajectories

8. Indexing Use R-tree to index the lines  Large MBRs, extensive overlap Use a Quadtree approach (or a grid) Partition the space into cells, store for each cell the lines that intersect it Disk space is increased

9. Dual space-time Idea: map a line to a point (y) location (t) time intercept slope intercept o o o o 1 2 3 4 o o o 1 2 3 trajectories

10. Dual space-time indexing Query must be transformed. [(y 1q, y 2q ), (t 1q, t 2q )] a + t 2q v >= y 1q and a+ t 1q v 0 a + t 1q v >= y 1q and a+ t 2q v <= y 2q, for v<0

11. Dual space-time indexing Another transformation (Hough-Y) is: The difference is that we compute the intercept over a horizontal line Queries in the dual space are similar with the previous transformation

12. Hough-Y space

13. Querying the dual space Use a PAM to index the dual points, change the search function to find the points inside the query Problem: Partitioning is not aligned with the queries  many I/Os An idea is to try to store multiple structures, one for each set of queries with similar slope

14. Improving the query In the Hough-Y, the slope of the queries is y 1q – y r (or y 2q – y r ) time location query y1y1 y2y2 y3y3

15. Improving the query Compute the dual using multiple y-lines Store an R-tree for each line Given a query, find the line that is closer to the query and then use the corresponding index Thus, the query will appear as vertical as possible  better performance

16. Indexing in 2-dimensions The dual transformation is not natural Map the trajectories in a point in 4-d using the transformations on x-t and y-t planes Use the 1-d structures to answer a query Another approach: parametrized R-tree

17. TP R-tree Time-Parametrized R-tree Store the MBRs as functions of time The MBRs grow with time, at any time instant in the future we can compute the “MBR”