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Spatio-Temporal Databases

Spatio-Temporal Databases. Moving Objects. 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.

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Spatio-Temporal Databases

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  1. Spatio-Temporal Databases Moving Objects

  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, MV3R-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 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 trajectories o 1 o 2 o 3 o 4 (t) time

  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 intercept trajectories o o 1 1 o 2 o 3 o 4 o 2 o 3 (t) time slope intercept

  10. Dual space-time indexing • Query must be transformed. [(y1q, y2q), (t1q, t2q)] • a + t2qv >= y1q and a+ t1q v <= y2q , for v>0 • a + t1qv >= y1q and a+ t2q v <= y2q , 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 y1q – yr (or y2q – yr) location y3 y2 query y1 time

  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 can be extended to 2 dimensional points • 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

  17. Dual for 2-D Moving Objects • Using Hough-X: • Map a moving point p with location (px, py) and velocity (vx, vy) to the 4D point (vx, ax, vy, ay) • Query is also transformed to a linear constraint query: Q=[(x1q, x2q), (y1q, y2q), (t1q, t2q)] • ax + t2qvx >= x1q and ax+ t1q vx <= x2q • ay + t2qvy >= y1q and ay+ t1q vy <= y2q • x1qvy - y2qvx <= axvy – ayvx<= x2qvy -y1q vx

  18. 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”

  19. Motion function • For each object, the database stores • Its minimum bounding rectangle (MBR) at the reference time 0 • Its current velocity bounding rectangle (VBR) • Examples: MBR(a)={2,4,3,4}, VBR(a)={1,1,1,1}; MBR(c)={8,9,8,9} • An update is necessary only when an object’s VBR changes.

  20. (a) The boundaries at current time 0 (b) The boundaries at future time 1 TPR – MBRs

  21. Insertion and Deletion • Insertion and Deletion similar to R*-tree • The only difference is that you have to compute the values: margin, overlap, volume over time • Trick: try to optimize the structure for the next H time instants. • Another optimization: when you update an object, re-compute the MBR at the current time

  22. y o1 o2 o3 o4 t update time An example of update and re-computation of MBR (1D) Reference: Simonas Saltenis, Christian S. Jensen, Scott T. Leutenegger, Mario A. Lopez: Indexing the Positions of Continuously Moving Objects. SIGMOD Conference 2000: 331-342

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