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Spatio-Temporal Databases

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Database stores the current location of each object and the ... Simonas Saltenis, Christian S. Jensen, Scott T. Leutenegger, Mario A. Lopez: Indexing the ... – PowerPoint PPT presentation

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Title: Spatio-Temporal Databases


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 ObjectsRepresentation
  • 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) vta

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 gt y1q and a t1q v lt y2q , for vgt0
  • a t1qv gt y1q and a t2q v lt y2q , for vlt0

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 gt x1q and ax t1q vx lt x2q
  • ay t2qvy gt y1q and ay t1q vy lt y2q
  • x1qvy - y2qvx lt axvy ayvxlt 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 objects VBR
    changes.

20
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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