1. Lecture 24: Query Execution
Wednesday, November 24, 2004

2. Outline
Query execution: 15.1 – 15.5

3. Two Pass Algorithms Based on Hashing
Idea: partition a relation R into buckets, on disk
Each bucket has size approx. B(R)/M
Does each bucket fit in main memory ?
Yes if B(R)/M <= M, i.e. B(R) <= M2
M main memory buffers
Disk
Relation R
OUTPUT 2
INPUT 1
hash
function h
M-1
Partitions
. . . 1 2
B(R)

4. Hash Based Algorithms for d
Recall: d(R) = duplicate elimination
Step 1. Partition R into buckets
Step 2. Apply d to each bucket (may read in main memory)
Cost: 3B(R)
Assumption:B(R) <= M2

5. Hash Based Algorithms for g
Recall: g(R) = grouping and aggregation
Step 1. Partition R into buckets
Step 2. Apply g to each bucket (may read in main memory)
Cost: 3B(R)
Assumption:B(R) <= M2

6. Partitioned Hash Join R |x| S Step 1: Step 2 Step 3
Hash S into M buckets
send all buckets to disk
Step 2
Hash R into M buckets
Send all buckets to disk
Step 3
Join every pair of buckets

7. Hash table for partition
Hash-Join
B main memory buffers
Disk
Original
Relation
OUTPUT 2
INPUT 1
hash
function h
M-1
Partitions
. . .
Partition both relations using hash fn h: R tuples in partition i will only match S tuples in partition i.
Partitions
of R & S
Input buffer
for Ri
Hash table for partition
Si ( < M-1 pages)
B main memory buffers
Disk
Output
buffer
Join Result
hash fn h2
Read in a partition of R, hash it using h2 (<> h!). Scan matching partition of S, search for matches. 14

8. Partitioned Hash Join Cost: 3B(R) + 3B(S)
Assumption: min(B(R), B(S)) <= M2

9. Hybrid Hash Join Algorithm
Partition S into k buckets
t buckets S1 , …, St stay in memory
k-t buckets St+1, …, Sk to disk
Partition R into k buckets
First t buckets join immediately with S
Rest k-t buckets go to disk
Finally, join k-t pairs of buckets:
(Rt+1,St+1), (Rt+2,St+2), …, (Rk,Sk)

10. Hybrid Join Algorithm How to choose k and t ?
Choose k large but s.t. k <= M
Choose t/k large but s.t t/k * B(S) <= M
Moreover: t/k * B(S) + k-t <= M
Assuming t/k * B(S) >> k-t: t/k = M/B(S)

11. Hybrid Join Algorithm How many I/Os ?
Cost of partitioned hash join: B(R) + 3B(S)
Hybrid join saves 2 I/Os for a t/k fraction of buckets
Hybrid join saves 2t/k(B(R) + B(S)) I/Os
Cost: (3-2t/k)(B(R) + B(S)) = (3-2M/B(S))(B(R) + B(S))

12. Hybrid Join Algorithm
Question in class: what is the real advantage of the hybrid algorithm ?

13. Indexed Based Algorithms
Recall that in a clustered index all tuples with the same value of the key are clustered on as few blocks as possible
Note: book uses another term: “clustering index”. Difference is minor…
a a a
a a a a a
a a

14. Index Based Selection Selection on equality: sa=v(R)
Clustered index on a: cost B(R)/V(R,a)
Unclustered index on a: cost T(R)/V(R,a)

15. Index Based Selection B(R) = 2000 T(R) = 100,000 V(R, a) = 20 Example:
Table scan (assuming R is clustered):
B(R) = 2,000 I/Os
Index based selection:
If index is clustered: B(R)/V(R,a) = 100 I/Os
If index is unclustered: T(R)/V(R,a) = 5,000 I/Os
Lesson: don’t build unclustered indexes when V(R,a) is small !
cost of sa=v(R) = ?

16. Index Based Join R S Assume S has an index on the join attribute
Iterate over R, for each tuple fetch corresponding tuple(s) from S
Assume R is clustered. Cost:
If index is clustered: B(R) + T(R)B(S)/V(S,a)
If index is unclustered: B(R) + T(R)T(S)/V(S,a)

17. Index Based Join
Assume both R and S have a sorted index (B+ tree) on the join attribute
Then perform a merge join
called zig-zag join
Cost: B(R) + B(S)