1. Spatial Join

2. Outline Relational Join Difference between relational and spatial join
Spatial Join using R-trees

3. Relational Join Basic Join Algorithm Input: Relations R and S
Output: Joined relation T
T=empty set
FOR EACH record r in R
FOR EACH record s in S
IF r.a==s.a
THEN append r||s to T
Complexity: O(|R||S|)
R S . : . :

4. More Efficient Join Hash-based join Sort-merge join
No need to sort both relations first.
Relations have hash indices.
Use hash to find the corresponding records.
Sort-merge join
Sort both relations first.
Scan through both relations only once.

5. Hash-based Join Input: Relations R and S Output: Joined relation T
T=empty set
FOR EACH record r in R
FOR EACH record s in hash(S, r.a)
IF r.a==s.a
THEN append r||s to T
Complexity: O(|R||bucket|)
R S . : . :

6. Sort-merge Join Input: Sorted relations R and S
Output: Joined relation T
T=empty set.
RP = pointer to the first record in R.
SP = pointer to the first record in S.
WHILE (RP is not null)
{ WHILE (*RP.a  *SP.a)
{ IF (*RP.a == *SP.a)
THEN add *RP||*SP to T
SP++ }
RP++
R S … a 2 3 5 8 … a 1 2 4 5 6 T 2 5
Complexity: O(|R|+|S|)

7. Spatial Join Hash-based join Sort-merge join
Spatial join using R-trees
Seeded trees
Sort-merge join
Iterative spatial join

8. Spatial Join Using R-trees
Input: nodes R, S in R-trees.
r_tree_join (R, S: node)
IF (R, S are leaf nodes)
THEN
RETURN all overlapping objects in R and S
FOR EACH r in R.children DO
FOR EACH s Î S.children DO
IF intersect (r,s)
THEN r_tree_join (r,s) ;

9. Example: Spatial Join Using R-trees

10. Seeded Trees
One relation, say R, has an R-tree as an index, but another relation, say S, has no index.
Create an R-tree for the relation S, using the structure of the R-tree for the relation R.
Advantage:
Minimize the number of overlapping MBRs for two trees.

11. Iterative Spatial Join
Similar to sort-merge join
Plane sweep method
Sort MBRs of objects in both relations by their lower bounds in the chosen dimension.
Initialize sweep structures of A and B
For each MBR X in the sorted list:
Update the sweep structure of the other relation.
Find MBRs in the sweep structure of other relation which overlaps X.
Good for limited main memory

12. Example:Iterative Spatial Join1 5 B 2 4 C 3 6 A D