CSIS 7101: Spatial Data (Part 2) Efficient Processing of Spatial Joins Using R-trees

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CSIS 7101Spatial Data (Part 2)Efficient
Processing of Spatial Joins Using R-trees

• Rollo Chan
• Chu Chung Man
• Mak Wai Yip
• Vivian Lee
• Eric Lo
• Sindy Shou
• Hugh Wang

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Efficient Processing of Spatial Join Using R-trees

• What is Spatial Data?
• Consists of points, lines, rectangles, polygons,
  surfaces
• Two types of queries in DBS
• Single scan and Multiple scan queries
• How to retrieve spatial objects in GIS
  efficiently?
• Spatial Access Method (SAM) eg. R-tree

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What is Spatial Access Method?

• Designed to support single scan query
• eg. Window query
• Find all objects which intersect a given window
• Attempts to store objects which are close
  together in the data space on a common page
• Reduces number of disk accesses

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How is window query processed by SAM?

• 1) Filter step
• Find all objects whose minimum bounding
  rectangles intersects the query rectangle
• 2) Refinement step
• Check whether the objects fulfill the query
  condition

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What is Spatial Join?

• To combine two sets of spatial objects according
  to some spatial properties
• It is an important type of query for multiple
  scanning in spatial DBS

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Example of Spatial Join

• Two relations forests, cities
• (Assume an attributes in each relation
  represents the borders of forests and cities)
• Example query would be
• Find all forests which are in a city

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Problems when performing Spatial Join

• It is too expensive in terms of CPU time and I/O
  time
• Traditional index structure is not efficient for
  spatial join
• How to make it more efficient?
• R-tree

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Why using R-tree for Spatial Join ?

• To optimize CPU-time and I/O time
• Less comparison than a simple nested loop
• Other algorithms cannot be efficiently applied to
  spatial join

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R-tree Approach for Spatial Join

• Suppose there are two R-trees
• R, S
• Idea
• To use the property that directory rectangles
  form the minimum bounding box of data rectangles
  in the corresponding subtrees.
• If the rectangles of two directory entries ER
  and ES have common intersection then there is a
  pair (rectR, rectS)

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Minimum Bounding Box
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Is there anyway to be more efficient?

• There are two areas we need to take into account
  in order to be more efficient
• CPU Time Tuning
• I/O Time Tuning

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CPU Time Tuning

• Two ways to improve CPU time
• Restricting the search space
• Spatial sorting and plane sweep

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Restricting the search space

• Idea
• Scan through each of two nodes marks all entries
  which are required for performing the join, (i.e.
  which intersect the intersecting rectangles of
  two nodes. )
• Then, each marked entry of one node is tested
  against all marked entries of the other node.

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Restricting the search space (contd)
Original 7 of R 7 of S
5
49 joins
1
4
6
2
2
1
1
5
1
3
2
6
2
3
7
Now 3 of R 2 of S
7
3
6 joins
Plus Scanning 7 of R 7 of S
4
14 times
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Spatial sorting and plane sweep

• Idea
• Sort the entries in a node of the R-tree
  according to the spatial location of the
  corresponding rectangles.
• Then move the Sweep-Line perpendicular to one of
  the axes from left to right to compute the
  intersections.

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Example of Sorted Intersection Test
r1.xu

• t r1 r1 lt--gt s1
• t s1 s1 lt--gt r2
• t r2 r2 lt--gt s2, r2 lt--gt s3
• t s2 -
• t r3 r3 lt--gt s3

s1.xl lt r1.xu
s1.xl
Sweep-Line
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I/O Time Tuning

• To achieve good I/O-performance with a buffer
  size as small as possible
• R-tree might occupy only small portion of
  LRU-buffer
• Compute a read schedule of the pages to minimize
  the number of disk accesses
• Local optimization policy based on spatial
  locality
• Idea of Read Schedule If a frequently used page
  always resides in the buffer, the number of disk
  access can be improved by a lot

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Three such techniques

• Local plane sweep
• Local plane sweep with pinning
• Local z-order

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Local Plane-Sweep Order

• Idea
• Based on spatial ordering, the plane-sweep
  algorithm creates a sequence of pairs of
  intersecting rectangles.
• This sequence can be used to determine the read
  schedule of the spatial join.

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Local Plane-Sweep Order (contd)

• Read schedule

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r3
r3
4
s2
s2
lt
gt
,
,
,
,
,
3
r1
r1
r4
r4
s1
s1
5
r2
1
r2
2
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Local Plane-Sweep Order w/ Pinning

• Idea
• Determine a pair of (Er,Es) of entries wrt local
  plane sweep order. Compute the degree of the
  rectangles of both entries
• Deg(E.rect) of intersections between E.rect
  and the rectangles which belong to entries of the
  other tree that are not yet processed
• Pin the page in the buffer whose corresponding
  rectangle has maximal degree
• Perform spatial join on the pinned page with all
  other pages

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Local Plane-Sweep Order w/ Pinning (contd)
Er.rect r1 Es.rect s2
r3
Es
1
s2
0
2
Deg(r1)
Deg(s2)
2
Er
r1
r4
s1
r2
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Local Z-Order

• Idea
• Compute the intersections between each rectangle
  of the one node and all rectangles of the other
  node
• Sort the rectangles according to the spatial
  location of their centers
• Decompose the underlying space into cells of
  equal size and provide an ordering on this set of
  cells

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Local Z-Order (contd)
r3
III
III
s2
IV
IV
II
II
r1
r4
s1
I
I
r2
Read schedule lts1,r2,r1,s2,r4,r3gt
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Number of Disk Access
gt
5384
5290
Size of LRU Buffer
lt
2392
2373
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Number of Disk Access (contd)
Size of LRU Buffer
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Q A

• Thats it for the Presentation
• Any Questions?

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Reference

1. Brinkhoff T., Kriegel H.P., Seeger B. (1993).
   Institute of Computer Science, University of
   Munich. Efficient Processing of Spatial Joins
   Using R-trees. Washington, DC, USA ACM-SIGMOD.