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