Planning with Polyalgebra: Bringing Together Relational, Complex and Machine Learning Algebra

© Hortonworks Inc. 2016
Polyalgebra
Hadoop Summit, April 14, 2016

Julian Hyde @julianhyde
Apache Calcite (VP), Drill, Kylin
Mondrian OLAP
Hortonworks
Thanks:
Jacques Nadeau @intjesus (Dremio/Drill)
Wes McKinney (Cloudera/Arrow)
Who
Tomer Shiran @tshiran
Apache Drill
Dremio

Page‹#› © Hortonworks Inc. 2014
Polyalgebra
An extended form of relational
algebra that encompasses work with
dynamically-typed data, complex
records, streaming and machine
learning that allows for a single
optimization space.

Ecosystem
Calcite
Drill
Arrow
Ibis
Impala
Kudu
Splunk
Cassandra
JDBC
MongoDB
JDBC
Spark
Flink

Ecosystem - data stores
Calcite
Drill
Arrow
Ibis
Impala
Kudu
Splunk
Cassandra
JDBC
MongoDB
JDBC
Spark
Flink

Ecosystem - Engines
Calcite
Drill
Arrow
Ibis
Impala
Kudu
Splunk
Cassandra
JDBC
MongoDB
JDBC
Spark
Flink

Ecosystem - Focus of this talk
Calcite
Drill
Arrow
Ibis
Impala
Kudu
Splunk
Cassandra
JDBC
MongoDB
JDBC
Spark
Flink

HadoopRDBMS
Old world, new world
• Security
• Metadata
• SQL
• Query planning
• Data independence
• Scale
• Late schema
• Choice of front-end
• Choice of engines
• Workload: batch, interactive,
streaming, ML, graph, …

Many front ends, many engines
SQL
Planning
Execution 
engine
Planning
User code
Map 
Reduce
Tez User code
in Yarn
Spark MongoDB
Hadoop
External 
SQL
SQL Spark Storm Cascading HBase Graph

Extension to mathematical set theory
Devised by E.F. Code (IBM) in 1970
Defines the relational database
Operators: select, filter, join, sort, union, etc.
Intermediate format for query planning/optimization
Relational algebra
SQL
Relational
algebra
Runnable
query
plan
Optimization

select d.name, COUNT(*) as c 
from Emps as e 
join Depts as d 
on e.deptno = d.deptno 
where e.age < 30 
group by d.deptno 
having count(*) > 5 
order by c desc
Relational algebra
Scan [Emps] Scan [Depts]
Join [e.deptno 
= d.deptno]
Filter [e.age < 30]
Aggregate [deptno, COUNT(*) AS c]
Filter [c > 5]
Project [name, c]
Sort [c DESC]
(Column names are simplified. They would usually 
be ordinals, e.g. $0 is the first column of the left input.)

select * from ( 
select zipcode, state 
from Emps 
union all 
select zipcode, state 
from Customers) 
where state in (‘CA’, ‘TX’)
Relational algebra - Union and sub-query
Scan [Emps] Scan [Customers]
Union [all]
Project [zipcode, state] Project [zipcode, state]
Filter [state IN (‘CA’, ‘TX’)]

insert into Facts 
values (‘Meaning of life’, 42), 
(‘Clever as clever’, 6)
Relational algebra - Insert and Values
Insert [Facts]
Values [[‘Meaning of life’, 42],
[‘Clever as clever’, 6]]

MySQL
Splunk
Expression tree  select p.productName, COUNT(*) as c 
from splunk.splunk as s 
join mysql.products as p 
on s.productId = p.productId 
where s.action = 'purchase' 
group by p.productName 
order by c desc
join
Key: product_id
group
Key: product_name 
Agg: count
filter
Condition: 
action = 
'purchase'
sort
Key: c DESC
scan
scan
Table: splunk
Table: products

Splunk
Expression tree 
(optimized)
join
Key: product_id
group
Key: product_name 
Agg: count
filter
Condition: 
action = 
'purchase'
sort
Key: c DESC
scan
Table: splunk
MySQL
scan
Table: products
select p.productName, COUNT(*) as c 
from splunk.splunk as s 
join mysql.products as p 
on s.productId = p.productId 
where s.action = 'purchase' 
group by p.productName 
order by c desc

Page‹#› © Hortonworks Inc. 2014
Demo
{sqlline, apache-calcite, .csv, CsvPushProjectOntoTableRule}

Calcite – APIs and SPIs
Cost, statistics
RelOptCost
RelOptCostFactory
RelMetadataProvider
• RelMdColumnUniquensss
• RelMdDistinctRowCount
• RelMdSelectivity
SQL parser
SqlNode 
SqlParser 
SqlValidator
Transformation rules
RelOptRule
• MergeFilterRule
• PushAggregateThroughUnionRule
• 100+ more
Global transformations
• Unification (materialized view)
• Column trimming
• De-correlation
Relational algebra
RelNode (operator)
• TableScan
• Filter
• Project
• Union
• Aggregate
• …
RelDataType (type)
RexNode (expression)
RelTrait (physical property)
• RelConvention (calling-convention)
• RelCollation (sortedness)
• TBD (bucketedness/distribution)
JDBC driver
Metadata
Schema
Table
Function
• TableFunction
• TableMacro
Lattice

Calcite Planning Process
SQL
parse
tree
Planner
RelNode
Graph
Sql-to-Rel Converter
SqlNode !
RelNode + RexNode
• Node for each node in
Input Plan
• Each node is a Set of
alternate Sub Plans
• Set further divided into
Subsets: based on traits
like sortedness
1. Plan Graph
• Rule: specifies an Operator
sub-graph to match and
logic to generate equivalent
‘better’ sub-graph
• New and original sub-graph
both remain in contention
2. Rules
• RelNodes have Cost &
Cumulative Cost
3. Cost Model
- Used to plug in Schema,
cost formulas
- Filter selectivity
- Join selectivity
- NDV calculations
4. Metadata Providers
Rule Match Queue
- Add Rule matches to Queue
- Apply Rule match
transformations to plan graph
- Iterate for fixed iterations or until
cost doesn’t change
- Match importance based on
cost of RelNode and height
Best RelNode Graph
Translate to
runtime
Logical Plan
Based on “Volcano” & “Cascades” papers [G. Graefe]

Algebra builder API
produces
final FrameworkConfig config;
final RelBuilder builder = RelBuilder.create(config);
final RelNode node = builder
.scan("EMP")
.aggregate(builder.groupKey("DEPTNO"),
builder.count(false, "C"),
builder.sum(false, "S", builder.field("SAL")))
.filter(
builder.call(SqlStdOperatorTable.GREATER_THAN,
builder.field("C"),
builder.literal(10)))
.build();
System.out.println(RelOptUtil.toString(node));
select deptno, 
COUNT(*) as c,
sum(sal) as s 
from Emp 
having COUNT(*) > 10
LogicalFilter(condition=[>($1, 10)])
LogicalAggregate(group=[{7}], C=[COUNT()], S=[SUM($5)])
LogicalTableScan(table=[[scott, EMP]])
Equivalent SQL:

Non-relational, post-relational
Non-relational stores:
• Document databases — MongoDB
• Key-value stores — HBase, Cassandra
• Graph databases — Neo4J
• Multidimensional OLAP — Microsoft Analysis, Mondrian
• Streams — Kafka, Storm
• Text, audio, video
Non-relational operators — data exploration, machine learning
Late or no schema

Complex data, also known as nested or
document-oriented data. Typically, it can be
represented as JSON. 
 
2 new operators are sufficient:
• UNNEST
• COLLECT aggregate function
Complex data employees: [
{
name: “Bob”,
age: 48,
pets: [
{name: “Jim”, type: “Dog”},
{name: “Frank”, type: “Cat”}
]
}, {
name: “Stacy",
age: 31, 
starSign: ‘taurus’,
pets: [
{name: “Jack”, type: “Cat”}
]
}, {
name: “Ken”,
age: 23
}
]

Flatten converts arrays of values to
separate rows:
• New record for each list item
• Empty lists removes record
Flatten is actually just syntactic sugar for
the UNNEST relational operator:
UNNEST and Flatten
name age pets
Bob 48 [{name: Jim, type: dog},
{name:Frank, type: dog}]
Stacy 31 [{name: Jack, type: cat}]
Ken 23 []
name age pet
Bob 48 {name: Jim, type: dog}
Bob 48 {name: Frank, type: dog}
Stacy 31 {name: Jack, type: cat}
select e.name, e.age, 
flatten(e.pet) 
from Employees as e
select e.name, e.age, 
row(a.name, a.type) 
from Employees as e,  
unnest e.addresses as a

Optimizing UNNEST
As usual, to optimize, we write planner rules.
We can push filters into the non-nested side,
so we write FilterUnnestTransposeRule.
(There are many other possible rules.)
select e.name, a.name 
from Employees as e,  
unnest e.pets as a
where e.age < 30
select e.name, a.street 
from ( 
select * 
from Employees  
where e.age < 30) as e,
unnest e.addresses as a
FilterUnnestTransposeRule

Optimizing UNNEST (2)
We can also optimize projects.
If table is stored in a column-oriented file
format, this reduces disk reads significantly.
• Array wildcard projection through flatten
• Non-flattened column inclusion
select e.name, 
flatten(pets).name 
from Employees as e
scan(name, age, pets)
flatten(pets) as pet
project(name, pet.name)
scan(name, pets[*].name)
flatten(pets) as pet
scan(name, age, pets)
flatten(pets as pet)
project(name, pets[*].name)
Original Plan Project through Flatten
Project into scan
(less data read)
ProjectFlattenTransposeRule ProjectScanRule

Evolution:
• Oracle: Schema before write, strongly typed SQL (like Java)
• Hive: Schema before query, strongly typed SQL
• Drill: Schema on data, weakly typed SQL (like JavaScript)
Late schema
name age starSign pets
Bob 48 [{name: Jim, type: dog},
{name:Frank, type: dog}]
Stacy 31 Taurus [{name: Jack, type: cat}]
Ken 23 []
name age pets
Ken 23 []
select * 
from Employees
select * 
from Employees
where age < 30
no starSign column!

Expanding *
• Early schema databases expand * at planning time, based on schema
• Drill expands * during query execution
• Each operator needs to be able to propagate column names/types as well as data
Internally, Drill is strongly typed
• Strong typing means efficient code
• JavaScript engines do this too
• Infer type for each batch of records
• Throw away generated code if a column changes type in the next batch of records
Implementing schema-on-data
select e.name 
from Employees
where e.age < 30
select e._map[“name”] as name 
from Employees
where cast(e._map[“age”] as integer) < 30

A table function is a Java UDF that returns a
relation.
• Its arguments may be relations or scalars.
• It appears in the execution plan.
• Annotations indicate whether it is safe to
push filters, project through
A table macro is a Java function that takes a
parse tree and returns a parse tree.
• Named after Lisp macros.
• It does not appear in the execution plan.
• Views (next slide) are a kind of table macro.
Use a table macro rather than a table function,
if possible. Re-use existing optimizations.
User-defined operators
select e.name 
from table(
my_sample(
select * from Employees,
0.15))
select e.name 
from table(
my_filter(
select * from Employees,
‘age’, ‘<‘, 30))

Views
Scan [Emps]
Join [$0, $5]
Project [$0, $1, $2, $3]
Filter [age >= 50]
Aggregate [deptno, min(salary)]
Scan [Managers]
Aggregate [manager]
Scan [Emps]
select deptno, min(salary) 
from Managers
where age >= 50
group by deptno
create view Managers as
select *
from Emps as e
where exists (
select *
from Emps as underling
where underling.manager = e.id)

Views (after expansion)
from Managers
where age >= 50
group by deptno
select *
from Emps as e
where exists (
select *
where underling.manager = e.id)
Scan [Emps] Aggregate [manager]
Join [$0, $5]
Project [$0, $1, $2, $3]
Filter [age >= 50]
Scan [Emps]

Views (after pushing down filter)
from Managers
where age >= 50
group by deptno
select *
from Emps as e
where exists (
select *
where underling.manager = e.id) Scan [Emps]
Scan [Emps]
Join [$0, $5]
Project [$0, $1, $2, $3]
Filter [age >= 50]

Materialized view
create materialized view 
EmpSummary as 
select deptno, 
gender, 
count(*) as c,  
sum(sal) 
from Emps
group by deptno, gender
select count(*) as c 
from Emps
where deptno = 10
and gender = ‘M’
Scan [Emps]
Aggregate [deptno, gender, 
COUNT(*), SUM(sal)]
Scan [EmpSummary] =
Scan [Emps]
Filter [deptno = 10 AND gender = ‘M’]
Aggregate [COUNT(*)]

Materialized view, step 2: Rewrite query to match
EmpSummary as 
select deptno, 
gender, 
count(*) as c,  
sum(sal) 
from Emps
from Emps
where deptno = 10
Scan [Emps]
COUNT(*), SUM(sal)]
Scan [EmpSummary] =
Scan [Emps]
COUNT(*) AS c, SUM(sal) AS s]
Project [c]

Materialized view, step 3: substitute table
EmpSummary as 
select deptno, 
gender, 
count(*) as c,  
sum(sal) 
from Emps
from Emps
where deptno = 10
Scan [Emps]
COUNT(*), SUM(sal)]
Scan [EmpSummary] =
Project [c]
Scan [EmpSummary]

Streaming queries run forever.
Stream appears in the FROM clause: Orders.
Without the stream keyword, Orders means the
history of the stream (a table).
Calcite streaming SQL: in Samza, Storm, Flink.
Streaming queries
select stream * 
from Orders
select * 
from Orders

• Orders is used as both stream and table
• System determines where to find the records
• Query is invalid if records are not available
Combining past and future
select stream * 
from Orders as o 
where units > (  
select avg(units) 
from Orders as h 
where h.productId = o.productId 
and h.rowtime > 
o.rowtime - interval ‘1’ year)

Hybrid systems combine more than one data source and/or engine.
Examples:
• Splunk join to MySQL
• User-defined table written in Python reading from an in-memory temporary table just
created by Drill.
• Streaming query populating a table summarizing the last hour’s activity that will be
used to populate a pie chart in a web dashboard.
Two challenges:
• Planning the query to take advantage of each system’s strengths.
• Efficient interchange of data at run time.
Hybrid systems

Hybrid algebra, hybrid run-time
Calcite
Drill
Arrow
Ibis
Impala
Kudu
Splunk
Cassandra
JDBC
MongoDB
JDBC
Spark
Flink

DREMIO© Hortonworks Inc. 2016
Arrow in a Slide
• New Top-level Apache Software Foundation project
– Announced Feb 17, 2016
• Focused on Columnar In-Memory Analytics
1. 10-100x speedup on many workloads
2. Common data layer enables companies to choose best of breed
systems
3. Designed to work with any programming language
4. Support for both relational and complex data as-is
• Developers from 13+ major open source projects involved
– A significant % of the world’s data will be processed through Arrow!
Calcite
Cassandra
Deeplearning4j
Drill
Hadoop
HBase
Ibis
Impala
Kudu
Pandas
Parquet
Phoenix
Spark
Storm
R

Focus on CPU Efficiency
Traditional
Memory Buffer
Arrow
Memory Buffer
• Cache Locality
• Super-scalar & vectorized
operation
• Minimal Structure Overhead
• Constant value access
– With minimal structure
overhead
• Operate directly on columnar
compressed data

High Performance Sharing & Interchange
Today With Arrow
• Each system has its own internal memory
format
• 70-80% CPU wasted on serialization and
deserialization
• Similar functionality implemented in
multiple projects
• All systems utilize the same memory
format
• No overhead for cross-system
communication
• Projects can share functionality (eg,
Parquet-to-Arrow reader)

• Algebra-centric approach
• Optimize by applying transformation rules
• User-defined operators (table functions, table macros, custom
RelNode classes)
• Complex data
• Late-schema queries
• Streaming queries
• Calcite enables planning hybrid queries
• Arrow enables hybrid runtime
Summary

@julianhyde
@tshiran
@ApacheCalcite
@ApacheDrill
@ApacheArrow
Get involved:
• http://calcite.apache.org
• http://drill.apache.org
• http://arrow.apache.org
Thanks!

Planning with Polyalgebra: Bringing Together Relational, Complex and Machine Learning Algebra

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Planning with Polyalgebra: Bringing Together Relational, Complex and Machine Learning Algebra