Top-k Spatial Joins
Po-Sung
[email protected]
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Survey
What’s top-k spatial joins
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What’s top-k spatial joins
Map overlays incur high execution cost
Retrieve the k objects
B
A
The processing of such this is expensive
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Top-k Spatial Joins
Apply a conventional spatial join
algorithm on the two data sets A and B
Count the number of output pairs in
which each object participates
Return the k objects with the maximum
intersection counts
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Top-1 join
< id , count , IL >
{A1 , 3 , [B1 , B2 , B3]}
B1
A1
{a1 , 3 , [b1 , b5 , b10]}
b1
B3
b5
a1
b10
A2
B2
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Definition 1
maxnum(e)  C
e.level
E is an intermediate entry of Ra
C the node capacity
e.level the level of the node that contains e
Upper bound maxnum(e)
for the number of objects in the subtree of e
maxnum( A1 )  5
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Definition 2
count (e) 

ei Rb and ei intersects e
maxnum(ei )
If e is leaf entry of Ra
• the number of objects of Rb that intersect
If e is intermediate entry
• upper bound of the actual count of any object in e
count ( A1 )  3  5  15
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Example
A1.IL
A2.IL
B1.IL
B5.IL
= [B1 , B2 , B5]
= [B5]
A1
= [A1]
= [A1 , A2]
B1
B5
A2
B2
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Example (cont.)
Heap H
E : <e , count , list>
e is the entry (of Ra or Rb)
count (e)  
list is e.IL
ei  e.IL
maxnum(ei )
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Example (cont.)
a1.IL= [b1 , b5 , b10]
a1.key=3
A2.IL= [b5]
a2.key=1
A1
B1
a2 b5
b1
a1
B3
b10
A2
B2
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Pseudocode
•For each
ei  i.IL
TS
(Rtree R , Rtree Rb, int by
k) e
•Join n and na // n is pointed
i
i
i
Join RTa and RTb to get intersecting pair (ea,eb)
•For each intersecting entry pair(e’, e’i) //
For each entry e that appears in a pair
build e’
e.IL,
compute e.count and insert
•Add
i to r’.IL
<e, ecount, e.IL>to a heap H (sorted by e.count)
•Compute e’.count
While number of reported objects < k
•If e’.count
> pruning condition
• e = de-heap(H)
• If e is a leaf
// actual
object found so far
//ie...count
ofentry
the k-th
best object
– Report (<e.id, e.count, e.IL>)
•Insert <e’, e’.count, e’IL> to H
• Else // e is an intermediate entry pointing to node n
•If e’ is a leaf entry //object
•Update pruning condition
•return
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Algorithm
Visiting order
count
Pruning
condition
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Multiple Expansions Method (ME)
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Two binary search trees
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Full join VS. Semi join
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Comparison environment
1. MCB x LA returns 16,477,244 intersection pairs
2. SKEW x LA returns 19,657,973 intersection pairs
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Node accesses versus k (full join).
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CPU time versus k (full join).
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Total cost versus k
(full join, 10 percent cache).
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Node accesses versus k (semijoin).
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CPU time versus k (semijoin).
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Total cost versus k
(semijoin, 10 percent cache).
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Conclusions
Bottom-k queries
Top-k distance (semi) join
Top-k nearest neighbor (semi) joins
Computing the NN (in A) of all objects of B
Sorting the resulting pairs (ob, oa) where oa
the NN of ob  B with respect to oa
Reporting the top-k objects of A
A
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in