Beyond EXPLAIN: Query Optimization From Theory To Code

Beyond EXPLAIN
Yuto Hayamizu
Ryoji Kawamichi
Query Optimization
From Theory To Code
2016/5/20
PGCon 2016 @ Ottawa

Before Relational …
• Querying was physical
• Need to understand
physical organization
• Navigate query execution
by yourself
2016/5/20 2
DEPT
EMP
PROJ
“Which file is this table stored in?”
“How are records linked?”
“Which access path is fast for this table?”
“What is the best order of joining tables”
…
Historically …

Before Relational …
• Querying was physical
• Need to understand
physical organization
• Navigate query execution
by yourself
2016/5/20 3
After Relational …
DEPT
EMP
PROJ
“Which file is this table stored in?”
“How are records linked?”
“Which access path is fast for this table?”
“What is the best order of joining tables”
…
• Querying is logical
• Physical organization is
black-boxed
• Just declare what you want
Historically …

Fill the Gap: Physical and Logical
2016/5/20 4
SELECT * FROM DEPT D, EMP E
WHERE E.D_ID = D.ID AND ...
• Storage I/O strategy
• Access path selection
• Join method selection
• Aggregation, sorting
• Resource allocation
• ...
Query Optimizer

If optimizer perfectly fills the gap...
2016/5/20 5
We don’t need EXPLAIN

Reality Is Tough
• Optimizer is NOT PERFECT
• Generated plans are not always optimal, sometimes
far from optimal
• We have to take care of physical behavior
• That’s why EXPLAIN is so much explained
2016/5/20 6

Go Beyond EXPLAIN
• Deeper understanding of optimization, better
control of your databases
• Theoretical fundamentals of query optimization
• From basic framework to cutting-edge technologies
• PostgreSQL Optimizer implementation
• Focusing on basic scan and join methods
• Behavior observation with TPC-H benchmark
2016/5/20 7

Outline
• Introduction
• Theory: Query Optimization Framework
• Code: PostgreSQL Optimizer
• Theory: Cutting-Edge Technologies Overview
• Summary
2016/5/20 8

Query Optimization Framework
• Cost-based optimization
• Plan selection with estimated execution cost
• Most of modern optimizers, including PostgreSQL,
are cost-based
• Rule-based optimization
• Plan selection with heuristically ranked rules
• Easy to produce the same result
• Hard to evaluate wide variety of plans
• Ex) Oracle (~10g), Hive (~0.13)
2016/5/20 9

Main Challenges in Cost-based Optimization
• Cost modeling is HARD
• Overhead of CPU, I/O, memory access, network, …
• Cardinality estimation is HARD
• Output size of scans, joins, aggregations, …
• Join ordering search is HARD
• Combinatorial explosion of join ordering and access path
• Exhaustive search is NP-hard
2016/5/20 10

System-R optimizer (1979)
• “The standard”
• Cost estimation with I/O and CPU
• Cardinality estimation with table statistics
• Bottom-up plan search
• Many of modern optimizers are “System-R style”
• PostgreSQL, MySQL, DB2, Oracle, ...
2016/5/20 11

Cost/Cardinality Estimation
• [#page fetched],[#storage API calls]
are estimated with cost formula and following
statistics
2016/5/20 12
CPU costI/O cost
COST = [#page fetched] + W * [#storage API calls]
weight parameter
• NCARD(T) ... the cardinality of relation T
• TCARD(T) ... the number of pages in relation T
• ICARD(I) ... the number of distinct keys in index I
• NINDX(I) ... the number of pages in index I

Bottom-up Plan Search
• Candidate plans for single relation
• The cheapest access path
• N-relation join ordering search
• Select the cheapest plans for each relation
• Then, find optimal join orderings of every 2-relation join
• Then, find optimal join orderings of every 3-relation join
• ... until N-relation
2016/5/20 13

Volcano/Cascades (1993)
• Top-down transformational plan search
• Yet another optimization approach
• Not well known as “System-R style”, but widely used in
practice
Ex) SQL Server, Apache Hive (Apache Calcite), Greenplum
Orca
• Extensible optimization framework
2016/5/20 19

Extensible Optimization Framework
Query Optimizer Generator
• Generalized expression of query plan not limited
to relational data model
• Users (optimizer developers) defines actual
implementations:
• Logical operator ... corresponds to relational algebra
• Physical algorithm ... corresponds to scan & join
methods such as sequential scan, index scan, hash
join, nested loop join
2016/5/20 20

Top-down Transformational Search
• Starts from an initial “logical plan”
• Generate alternative plans with:
A) Logical operator transformation
B) Physical algorithm selection
C) Enforcing sorting order
2016/5/20 21
Join Select T
Join
Select R Select S
Proj
Join
Select T
JoinSelect R
Select S
Proj
Change join ordering
Join Select T
Join
Select R
Select SProj
Projection push down
Example: 3-way join with projection

2016/5/20 22
Join Select T
Join
Select R Select S
ProjExample: 3-way join with projection
HashJoin Select T
Join
SeqScan R SeqScan S
Proj
Join IdxScan T
Join
Select R Select S
Proj
…

2016/5/20 23
Join Select T
Join
Select R Select S
Proj
Example: 3-way join with projection
Join Select T
Join
Sort Sort
Proj
Select R Select S
Enforce sorting order
merge join of R and S is possible now

Benefits of Top-down approach
• Possible to intentionally limit search space
• Effective pruning with branch-and-bound
• Limit search space with search time deadline
2016/5/20 24

Cost-based Optimization Basics
Two major cost-based optimization style
• System-R
• Cost modeling with statistics
• Bottom-up search
• Volcano/Cascades
• Extensible optimizer generator
• Cost estimation is user’s responsibility
• Top-down transformational search
2016/5/20 25

Outline
• Introduction
• Summary
2016/5/20 26

PostgreSQL Optimizer
“System-R style” optimization
• Bottom-up plan search with dynamic programming
• CPU and I/O operation based cost modeling
2016/5/20 27
Seq. I/O Random I/O CPU cost per tuple
Cost of single operation
• seq_page_cost
• random_page_cost
• cpu_tuple_cost
• cpu_index_tuple_cost
• cpu_operator_cost
• (parallel_tuple_cost)
Estimated number of each operation
• Cardinality estimation with
statistics
• Cost formula for each plan type
• SeqScan, IndexScan
• NestLoopJoin, HashJoin,
MergeJoin, ...

Detailed Look At Basic Scan Types
• Sequential scan
• Efficient for accessing large potion of tables
• Index scan
• Efficient for accessing a fraction of data
2016/5/20 28
Execution cost
Query selectivity
Sequential scan

of SeqScan
29
= (# pages in a table)
= (# tuples in a table)
= #qual_operator
= (#tuples) × (weight factor of A)
+ (#tuples) × (weight factor of B)
+ ・・・
・・・ WHERE AND AND ・・・A B
cost_seqscan()
@optimizer/path/costsize.c

of IndexScan
Consists of:
(A) CPU cost of searching B+-tree
(B) CPU cost of scanning index tuples in leaf pages
(C) I/O cost of leaf pages
(D) I/O cost of heap pages
(E) CPU cost of scanning heap tuples
2014/12/04 30

of IndexScan
(A) B+-tree search
(B) Scanning index tuples in leaf pages
2014/12/04 31
+= log2(#index_tuples)
I/O cost of internal pages
Assumed to be always cached in the buffer
+= #qual_operator
× #leaf_pages ✕ #ituple_per_page × σ
Selectivity σ
Comes from statistics

Mackert and Lohman function（Yao function）
I/O count estimation with consideration of buffer caching
of IndexScan
(C) I/O cost of index leaf pages
2014/12/04 32
+= Y(effective_cache_size, #leaf_pages)
Selectivity σ
I/Ocount

of IndexScan
(D) I/O cost of heap pages
(E) CPU cost of scanning heap tuples
・ Estimate the number of scanned tuples from σ
2014/12/04 33
+= α2 × #match_pages
Correlation between index and heap ordering: α
α = 0 : I/O pattern is random α = 1 : I/O pattern is sequential
+= (1-α2) × #match_tuples

Detailed Look At Join Methods
• Hash join
• Efficient for joining large number of records
• Usually combined with sequential scans
• Nested Loop Join
• Efficient for joining small number of records
• Usually combined with index scans or small table
sequential scans
2016/5/20 34

of HashJoin
Build phase
• Cost += Cost(inner)
2014/12/04 36
+= #qual_op × #inner_tuples
+= #inner_tuples
Hashing cost

of HashJoin
2014/12/04 37
Build phase
• Cost += Cost(inner)
+= #inner_tuples

of HashJoin
2014/12/04 38
Build phase
• Cost += Cost(inner)+
Probe phase
• Cost += Cost(outer)+
+= #inner_tuples
+= #qual_op × (1 + #bucket_size × 0.5)
× #outer_tuples
+= #match_tuples
Hashing & table lookup (bucket search) cost

recordrecordrecordrecordrecordrecordrecordrecordrecordrecordrecordrecordrecordrecordrecordtuple
of HashJoin
2014/12/04 39
#buckets: 2 #buckets : 4
build
4 tuples are compared for
lookup in average 2 tuples are compared for lookup
in average
0.E+00
5.E+06
1.E+07
2.E+07
2.E+07
3.E+07
3.E+07
4.E+07
4.E+07
10000 100000 1000000 10000000 100000000
Estimated cost of 2-way HashJoin
# of records
16 records
recordrecordrecordrecordrecordrecordrecordtuple
recordrecordrecordrecordrecordrecordrecordtuple
recordrecordrecordtuple

of NestLoopJoin
2014/12/04 40
R ⨝ S Scan R r2
r1
r3
r4
Scan S with r1
s1
s2
s3
ReScan S with r2
s1
s2
s3
outer inner

of NestLoopJoin
• When #outer_tuples = 1
2014/12/04 41
R ⨝ S Scan R
r1
Scan S with r1
s1
s2
s3
outer inner
Cost = Cost(outer) + Cost(inner) +
+= #inner_tuples
+= #qual_operator × #inner_tuples

of NestLoopJoin
• When #outer_tuples > 1
R ⨝ S Scan R r2
r1
r3
r4
Scan S with r1
s1
s2
s3
ReScan S with r2
s1
s2
s3
outer inner
Cost = Cost(outer) + Cost(inner) +
+ (#outer_tuples - 1) × Cost(ReScan inner)
Higher buffer hit ratio in ReScan
→ Cost of ReScan is lower than cost of IndexScan
+= #inner_tuples × #outer_tuples
+= #qual_operator × #inner_tuples × #outer_tuples

See How It Works
• TPC-H Benchmark
• Specification and tools for benchmarking data
warehouse workload
• Open source implementation: DBT-3, pg_tpch
• Schema, data generation rules and queries
• Experiments with 100GB
• Scale Factor = 100
2016/5/20 43

Experimental Setup
• Dell R720xd
• Xeon (2sockets, 16cores)
• x24 NL-SAS HDD
• With PostgreSQL 9.5
• Default cost parameter settings
• SeqScan & HashJoin
• enable_seqscan = on, enable_hashjoin = on
and disables other methods
• IndexScan & NestLoopJoin
• enable_indexscan = on, enable_nestloop = on
and disables other methods
2016/5/20 44

TPC-H Q.1: The Simplest Case
2016/5/20 45
5.E+05
5.E+06
5.E+07
5.E+08
1 10 100 1000
Estimated cost
Selectivity (l_shipdate)
IndexScan
SeqScan
10
100
1000
10000
1 10 100 1000
Execution time (sec)
Selectivity(l_shipdate)
IndexScan
SeqScan
• Good trend estimation for each
method
• Estimated break-event point is
errorneus
• IndexScan should be more
expensive (need parameter
calibration)
SELECT count(*), ... FROM lineitem
WHERE l_shipdate BETWEEN [X] AND [Y]

TPC-H Q.3
2016/5/20 46
Estimated cost
SeqScan
customer
SeqScan
orders
SeqScan
lineitem
Hash
HashJoin
HashJoin
IndexScan
orders
IndexScan
lineitem
NestLoop
NestLoop
IndexScan
customer
Selectivity
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1 10 100 1000 10000 100000 1000000
1
10
100
1000
10000
1 10 100 1000 10000 100000 1000000
Selectivity
NestLoop+IndexScan
HashJoin+SeqScan
NestLoop+IndexScan
HashJoin+SeqScan Similar result as in Q.1
• Good trend estimation for each
• Erroneous break-event point
without parameter calibration
SELECT count(*), ...
FROM customer, orders, lineitem
WHERE c_custkey = o_custkey AND
o_orderkey = l_orderkey AND
c_custkey < [X] AND
c_mktsegment = ‘MACHINERY’;

100
1000
10000
100000
1 10 100 1000 10000
More Complex Case
TPC-H Q.4: Semi-Join Query
• Plan selection for semi-
join tend to be unstable
2016/5/20 47Selectivity
1.E+05
1.E+06
1.E+07
1.E+08
1.E+09
1 10 100 1000 10000
HashJoin+SeqScan
NestLoop+IndexScan
Estimated cost
HashJoin+SeqScan
NestLoop+IndexScan SELECT count(*), ...
FROM orders
WHERE
o_orderdate >= ‘1995-01-01’ AND
o_orderdate < ‘1995-01-01’
+ interval ‘3 month’ AND
EXISTS(
SELECT * FROM lineitem
WHERE l_orderkey = o_orderkey
AND l_commitdate < l_receiptdate)
Selectivity

1.E+06
1.E+07
1.E+08
1.E+09
1.E+10
1.E+11
1.E+00 1.E+02 1.E+04 1.E+06 1.E+08
More Complex Case
TPC-H Q.22: Anti-Join Query
• Difficulties in overall cost
trend estimation
2016/5/20 48
Selectivity
1
10
100
1000
10000
1.E+00 1.E+02 1.E+04 1.E+06 1.E+08
Estimated cost
Selectivity
HashJoin+SeqScan
NestLoop+IndexScan
HashJoin+SeqScan
NestLoop+IndexScan
SELECT count(*), ...
FROM supplier, lineitem l1, orders, nation
WHERE s_suppkey = l1.l_suppkey AND
o_orderkey = l1.l_orderkey AND
o_orderstatus = 'F' AND
l1.l_receiptdate > l1.l_commitdate AND
EXISTS (
SELECT * FROM lineitem l2
WHERE l2.l_orderkey = l1.l_orderkey
AND l2.l_suppkey <> l1.l_suppkey)
AND NOT EXIST (
SELECT * FROM lineitem l3
WHERE l3.l_orderkey = l1.l_orderkey
AND l3.l_suppkey <> l1.l_suppkey
AND l3.l_receiptdate > l3.l_commitdate)
AND s_nationkey = n_nationkey
AND n_name = ‘JAPAN'

Summary: PostgreSQL
Optimizer
• Detailed look at cost modeling of basic methods
• SeqScan, IndexScan
• HashJoin, NestedLoopJoin
• Observation with TPC-H benchmark
• Good cost trend estimation for simple join queries
• Erroneous cheapest plan selection without parameter tuning
• Difficulties with semi-join and anti-join queries
2016/5/20 49

Outline
• Introduction
• Summary
2016/5/20 50

Cutting-Edge Technologies
• Traditional optimization was a “closed” problem
• “Rethink the contract” ー Surajit Chaudhuri
• Feedback from previous execution
• Dynamic integration with execution
2016/5/20 51
cardinality
estimation
cost model
plan space
enumeration
(SQL) query plan

Mid-query Re-optimization
• Detects sub-optimality of executing query plan
• Query plans are annotated for later estimation
improvement
• Runtime statistics collection
• Statistics collector probes are inserted into operators of
executing query plan
• Plan modification strategy
• Discard current execution and re-optimize whole plan
• Re-optimizer only subtree of the plan that are not
started yet
• Save partial execution result and generate new SQL
using the result
2016/5/20 52
[N. Kabra et.al., SIGMOD’98]

Plan Bouquet
• Generate a set of plans for each selectivity range
• Estimation improvement with runtime statistics
collection
• Evaluation with PostgreSQL
2016/5/20 53
[A. Dutt et.al., SIGMOD’14]

Bounding Impact of Estimation Error
• “Uncertainty” analysis of cost estimation
• Optimality sensitivity to estimation error
• Execute partially to reduce uncertainty
2016/5/20 54
[T. Neumann et.al., BTW Conf ‘13]

Outline
• Introduction
• Summary
2016/5/20 55

Summary
• Cost-based optimization framework
• System-R style bottom-up optimization
• Volcano style top-down optimization
• Detailed look at PostgreSQL optimizer
• Cost modeling of basic scan and join method
• Experiment with TPC-H benchmark
• Brief overview of cutting-edge technologies
2016/5/20 56

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Beyond EXPLAIN: Query Optimization From Theory To Code