1. Faloutsos/Pavlo C. Faloutsos – A. Pavlo Lecture#13: Query Evaluation
CMU /615
Carnegie Mellon Univ. Dept. of Computer Science /615 - DB Applications
C. Faloutsos – A. Pavlo
Lecture#13: Query Evaluation

2. Today's Class Intro to Operator Evaluation Typical Query Optimizer
Faloutsos/Pavlo
CMU /615
Today's Class
Intro to Operator Evaluation
Typical Query Optimizer
Projection/Aggregation: Sort vs. Hash
Faloutsos/Pavlo
CMU SCS /615

3. Example Database STUDENT ENROLLED COURSE sid name login age gpa 53666
Faloutsos/Pavlo
CMU /615
Example Database
STUDENT
ENROLLED
sid
name
login
age
gpa
53666
Kayne 39
4.0
53688
Bieber 22
3.9
53655
Tupac 26
3.5
sid
cid
grade
53666
15-415 C
53688
15-721 A
15-826 B
53655
COURSE
cid
name
15-415
Database Applications
15-721
Database Systems
15-826
Data Mining
15-823
Advanced Topics in Databases
Faloutsos/Pavlo
CMU SCS /615

4. pname,cid (sgrade=‘A’ (student⋈enrolled))
Query Plan Example
SELECT name, cid
FROM student, enrolled
WHERE student.sid =
enrolled.sid
AND enrolled.grade = ‘A’
Relational Algebra:
pname,cid (sgrade=‘A’ (student⋈enrolled))
Faloutsos/Pavlo
CMU SCS /615

5. Query Plan Example p s ⨝ SELECT name, cid FROM student, enrolled
WHERE student.sid =
enrolled.sid
AND enrolled.grade = ‘A’
student
enrolled s ⨝ p
name, cid
grade=‘A’
sid=sid
Faloutsos/Pavlo
CMU SCS /615

6. Query Plan Example p s ⨝ SELECT name, cid FROM student, enrolled
WHERE student.sid =
enrolled.sid
AND enrolled.grade = ‘A’
“On-the-fly”
student
enrolled s ⨝ p
name, cid
“On-the-fly”
grade=‘A’
Hash Join
sid=sid
File Scan
File Scan
Faloutsos/Pavlo
CMU SCS /615

7. Query Plan Example p s ⨝ SELECT name, cid FROM student, enrolled
WHERE student.sid =
enrolled.sid
AND enrolled.grade = ‘A’
student
enrolled s ⨝ p
The output of each operator is the input to the next operator.
Each operator iterates over its input and performs some task.
Faloutsos/Pavlo
CMU SCS /615

8. After Midterm: How the DBMS finds the best plan.
Operator Evaluation
Several algorithms are available for different relational operators.
Each has its own performance trade-offs.
The goal of the query optimizer is to choose the one that has the lowest “cost”.
After Midterm: How the DBMS finds the best plan.
Faloutsos/Pavlo
CMU SCS /615

9. Operator Execution Strategies
Indexing
Iteration (= seq. scanning)
Partitioning (sorting and hashing)
Faloutsos/Pavlo
CMU SCS /615

10. Operator Algorithms Selection: file scan; index scan
Projection: hashing; sorting
Join: looping; hashing; sorting
Group By: hashing; sorting
Order By: sorting
Faloutsos/Pavlo
CMU SCS /615

11. Operator Algorithms Selection: file scan; index scan
Next Lecture
Selection: file scan; index scan
Projection: hashing; sorting
Join: looping; hashing; sorting
Group By: hashing; sorting
Order By: sorting
Today
Next Lecture
Today
Today
Faloutsos/Pavlo
CMU SCS /615

12. Today's Class Intro to Operator Evaluation Typical Query Optimizer
Faloutsos/Pavlo
CMU /615
Today's Class
Intro to Operator Evaluation
Typical Query Optimizer
Projection/Aggregation: Sort vs. Hash
Faloutsos/Pavlo
CMU SCS /615

13. Query Optimization Bring query in internal form (eg., parse tree)
… into “canonical form” (syntactic q-opt)
Generate alternative plans.
Estimate cost for each plan.
Pick the best one.
Faloutsos/Pavlo
CMU SCS /615

14. Query Plan Example p s ⨝ SELECT name, cid FROM student, enrolled
WHERE student.sid =
enrolled.sid
AND enrolled.grade = ‘A’
student
enrolled s ⨝ p
name, cid
grade=‘A’
sid=sid
Faloutsos/Pavlo
CMU SCS /615

15. Query Plan Example s ⨝ p s ⨝ p s ⨝ p SELECT name, cid
FROM student, enrolled
WHERE student.sid =
enrolled.sid
AND enrolled.grade = ‘A’
student
enrolled s ⨝ p
sid=sid
grade=‘A’
name, cid
student
enrolled s ⨝ p
sid=sid
grade=‘A’
name, cid
sid, cid
student
enrolled s ⨝ p
sid=sid
grade=‘A’
name, cid
Faloutsos/Pavlo
CMU SCS /615

16. Today's Class Intro to Operator Evaluation Typical Query Optimizer
Faloutsos/Pavlo
CMU /615
Today's Class
Intro to Operator Evaluation
Typical Query Optimizer
Projection/Aggregation: Sort vs. Hash
Faloutsos/Pavlo
CMU SCS /615

17. Duplicate Elimination
What does it do, in English?
How to execute it?
SELECT DISTINCT cid
FROM enrolled
WHERE grade IN (‘B’,’C’)
pDISTINCT cid (sgrade=‘B’ ∨ grade=‘C’ (enrolled))
Not technically correct because RA doesn’t have “DISTINCT”
Faloutsos/Pavlo
CMU SCS /615

18. Duplicate Elimination
SELECT DISTINCT cid
FROM enrolled
WHERE grade IN (‘B’,’C’)
enrolled s p
grade=‘B’ ∨ grade=‘C’
DISTINCT cid
Two Choices:
Sorting
Hashing
Faloutsos/Pavlo
CMU SCS /615

19. Sorting Projection p s X Filter Remove Columns Sort Eliminate Dupes
enrolled s p
grade=‘B’ ∨ grade=‘C’
DISTINCT cid
sid
cid
grade
53666
15-415 C
53688
15-721 A
15-826 B
53655
sid
cid
grade
53666
15-415 C
53688
15-826 B
15-721
53655
cid
15-415
15-826
15-721
cid
15-415
15-721
15-826 X
Filter
Remove Columns
Sort
Eliminate
Dupes
Faloutsos/Pavlo
CMU SCS /615

20. Alternative to Sorting: Hashing!
What if we don’t need the order of the sorted data?
Forming groups in GROUP BY
Removing duplicates in DISTINCT
Hashing does this!
And may be cheaper than sorting! (why?)
But what if table doesn’t fit in memory?
Faloutsos/Pavlo
CMU SCS /615

21. Hashing Projection
Populate an ephemeral hash table as we iterate over a table.
For each record, check whether there is already an entry in the hash table:
DISTINCT: Discard duplicate.
GROUP BY: Perform aggregate computation.
Two phase approach.
Faloutsos/Pavlo
CMU SCS /615

22. Phase 1: Partition
Use a hash function h1 to split tuples into partitions on disk.
We know that all matches live in the same partition.
Partitions are “spilled” to disk via output buffers.
Assume that we have B buffers.
Faloutsos/Pavlo
CMU SCS /615

23. Phase 1: Partition p s h1 ⋮ Filter Remove Columns Hash enrolled
grade=‘B’ ∨ grade=‘C’
DISTINCT cid
sid
cid
grade
53666
15-415 C
53688
15-721 A
15-826 B
53655
B-1 partitions
15-415 ⋮
15-826
15-721
sid
cid
grade
53666
15-415 C
53688
15-826 B
15-721
53655
cid
15-415
15-826
15-721 h1
Filter
Remove Columns
Hash
Faloutsos/Pavlo
CMU SCS /615

24. Phase 2: ReHash For each partition on disk:
Read it into memory and build an in-memory hash table based on a hash function h2
Then go through each bucket of this hash table to bring together matching tuples
This assumes that each partition fits in memory.
Faloutsos/Pavlo
CMU SCS /615

25. Phase 2: ReHash p s h2 h2 h2 ⋮ Hash Table Eliminate Dupes enrolled
grade=‘B’ ∨ grade=‘C’
DISTINCT cid
sid
cid
grade
53666
15-415 C
53688
15-721 A
15-826 B
53655
15-415 ⋮
15-826
15-721 h2
key
value
XXX
15-415
YYY
15-826
ZZZ
15-721
cid
15-415
15-826
15-721 h2
Partitions
From
Phase 1 h2
Hash
Table
Eliminate
Dupes
Faloutsos/Pavlo
CMU SCS /615

26. Analysis How big of a table can we hash using this approach?
B-1 “spill partitions” in Phase 1
Each should be no more than B blocks big
Faloutsos/Pavlo
CMU SCS /615

27. Analysis How big of a table can we hash using this approach?
B-1 “spill partitions” in Phase 1
Each should be no more than B blocks big
Answer: B∙(B-1).
A table of N blocks needs about sqrt(N) buffers
What assumption do we make?
Faloutsos/Pavlo
CMU SCS /615

28. Analysis How big of a table can we hash using this approach?
B-1 “spill partitions” in Phase 1
Each should be no more than B blocks big
Answer: B∙(B-1).
A table of N blocks needs about sqrt(N) buffers
Assumes hash distributes records evenly!
Use a “fudge factor” f >1 for that: we need
B ~ sqrt( f ∙N)
Faloutsos/Pavlo
CMU SCS /615

29. Analysis Have a bigger table? Recursive partitioning!
In the ReHash phase, if a partition i is bigger than B, then recurse.
Pretend that i is a table we need to hash, run the Partitioning phase on i, and then the ReHash phase on each of its (sub)partitions
Faloutsos/Pavlo
CMU SCS /615

30. Recursive Partitioning
Hash the overflowing bucket again h2 ⋮ h1
h1’
Hash
Faloutsos/Pavlo
CMU SCS /615

31. Hashing vs. Sorting Which one needs more buffers? Faloutsos/Pavlo
CMU SCS /615

32. Hashing vs. Sorting
Recall: We can hash a table of size N blocks in sqrt(N) space
How big of a table can we sort in 2 passes?
Get N/B sorted runs after Pass 0
Can merge all runs in Pass 1 if N/B ≤ B-1
Thus, we (roughly) require: N ≤ B2
We can sort a table of size N blocks in about space sqrt(N)
Same as hashing!
Faloutsos/Pavlo
CMU SCS /615

33. Hashing vs. Sorting
Choice of sorting vs. hashing is subtle and depends on optimizations done in each case
Already discussed optimizations for sorting:
Chunk I/O into large blocks to amortize seek+RD costs
Double-buffering to overlap CPU and I/O
Faloutsos/Pavlo
CMU SCS /615

34. Hashing vs. Sorting
Choice of sorting vs. hashing is subtle and depends on optimizations done in each case
Another optimization when using sorting for aggregation:
“Early aggregation” of records in sorted runs
Let’s look at some optimizations for hashing next…
Faloutsos/Pavlo
CMU SCS /615

35. Hashing: We Can Do Better!
Combine the summarization into the hashing process - How?
Faloutsos/Pavlo
CMU SCS /615

36. Hashing: We Can Do Better!
During the ReHash phase, store pairs of the form <GroupKey, RunningVal>
When we want to insert a new tuple into the hash table:
If we find a matching GroupKey, just update the RunningVal appropriately
Else insert a new <GroupKey, RunningVal>
Faloutsos/Pavlo
CMU SCS /615

37. Hashing Aggregation h2 h2 h2 ⋮ Hash Table Final Result
SELECT cid, AVG(s.gpa)
FROM student AS s, enrolled AS e
WHERE s.sid = e.sid
GROUP BY cid
Running Totals
15-415 ⋮
15-826
15-721 h2
key
value
XXX
<15-415, 2.99>
YYY
<15-826,3.76>
ZZZ
<15-721,3.44>
cid
AVG(gpa)
15-415
3.66
15-826
3.333
15-721
2.89 h2
Partitions
From
Phase 1 h2
Hash
Table
Final
Result
Faloutsos/Pavlo
CMU SCS /615

38. Hashing Aggregation What’s the benefit?
How many entries will we have to handle?
Number of distinct values of GroupKeys columns
Not the number of tuples!
Also probably “narrower” than the tuples
Faloutsos/Pavlo
CMU SCS /615

39. So, Hashing is Better…right?
Any caveats?
Sorting is better on non-uniform data.
Sorting is better when result needs to be sorted.
Hashing vs. sorting:
Commercial systems use either or both
Faloutsos/Pavlo
CMU SCS /615

40. Summary Query processing architecture:
Query optimizer translates SQL to a query plan
Query executor “interprets” the plan
Hashing is a useful alternative to sorting for duplicate elimination / group-by
Both are valuable techniques for a DBMS
Faloutsos/Pavlo
CMU SCS /615

41. Next Class How to actually use indexes. Join algorithms.
More query optimization.
Faloutsos/Pavlo
CMU SCS /615