Query Execution

Zachary G. IvesUniversity of Pennsylvania

CIS 650 – Implementing Data Management Systems

January 24, 2005

Content on hashing and sorting courtesy Ramakrishnan & Gehrke

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Today’s Trivia Question

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Query Execution

What are the goals? Logical vs. physical plans – what are the

differences?

Some considerations in building execution engines: Efficiency – minimize copying, comparisons Scheduling – make standard code-paths fast Data layout – how to optimize cache behavior,

buffer management, distributed execution, etc.

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Execution System Architectures

Central vs. distributed vs. parallel vs. mediator

Data partitioning – vertical vs. horizontal Monet model – binary relations Distributed – data placement

One operation at a time – INGRES Pipelined

Iterator-driven Dataflow-driven Hybrid approaches

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Execution Strategy Issues

Granularity & parallelism: Pipelining vs. blocking Materialization

Select

Client = “Atkins”

Join

PressRel.Symbol = Clients.Symbol

Scan

PressRel

Scan

Clients

Join

PressRel.Symbol = EastCoast.CoSymbol

Project

CoSymbol

Scan

EastCoast

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Iterator-Based Query Execution

Execution begins at root open, next, close Propagate calls to

childrenMay call multiple child nexts

“Synchronous pipelining”Minimize copies

Efficient scheduling & resource usage

Can you think of alternatives and their benefits?

Select

Client = “Atkins”

Join

PressRel.Symbol = Clients.Symbol

Scan

PressRel

Scan

Clients

Join

PressRel.Symbol = EastCoast.CoSymbol

Project

CoSymbol

Scan

EastCoast

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The Simplest Method

Iteration over tables Sequential scan Nested loops join

What’s the cost? What tricks might we use to speed it up?

Optimizations: Double-buffering

Overlap I/O and computation Prefetch a page into a shadow block while CPU processes

different block Requires second buffer to prefetch into Switch to that when the CPU is finished with the alternate

buffer

Alternate the direction of reads in file scan

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Speeding Operations over Data

Three general data organization techniques: Indexing

Associative lookup & synopses

Sorting Hashing

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Indices

GiST and B+ TreesAlternatives for storage:

<key, record>; <key, rid>; <key, {rids}>

Clustered vs. unclustered

Bitmapped index – bit position for each value in the domain Requires a domain with

discrete values (not necessarily ordinal)

Booleans; enumerations; range-bounded integers

Low-update data Efficient for AND, OR only

expressions between different predicates

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Usefulness of Indices

Where are these structures most useful? Sargable predicates Covering indices

In many cases, only help with part of the story Filter part of the answer set, but we still need

further computation e.g., AND or OR of two predicates

General rule of thumb: Unclustered index only useful if selectivity is <

10-20%

Sorting – External Binary Sort

Divide and conquer: sort into subfiles and merge

Each pass: we read & write every page

If N pages in the file, we need:

dlog2(N)e + 1

passes to sort the data, yielding a cost of:

2Ndlog2(N)e + 1

Input file

1-page runs

2-page runs

4-page runs

8-page runs

PASS 0

PASS 1

PASS 2

PASS 3

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3,4 6,2 9,4 8,7 5,6 3,1 2

3,4 5,62,6 4,9 7,8 1,3 2

2,34,6

4,7

8,91,35,6 2

2,3

4,46,7

8,9

1,23,56

1,22,3

3,4

4,56,6

7,8

General External Merge Sort

To sort a file with N pages using B buffer pages: Pass 0: use B buffer pages. Produce dN / Be sorted

runs of B pages each Pass 2, …, etc.: merge B-1 runs

B Main memory buffers

INPUT 1

INPUT B-1

OUTPUT

DiskDisk

INPUT 2

. . . . . .

. . .

How can we utilize more than 3 buffer pages?

Cost of External Merge Sort

Number of passes: 1+dlogB-1 dN / Bee Cost = 2N * (# of passes) With 5 buffer pages, to sort 108 page file:

Pass 0: d108/5e = 22 sorted runs of 5 pages each (last run is only 3 pages)

Pass 1: d22/4e = 6 sorted runs of 20 pages each (final run only uses 8 pages)

Pass 2: d6/4e = 2 sorted runs, 80 pages and 28 pages

Pass 3: Sorted file of 108 pages

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Applicability of Sort Techniques

Join Intersection Aggregation

Duplicate removal as an instance of aggregation

XML nesting as an instance of aggregation

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Merge Join

Requires data sorted by join attributesMerge and join sorted files, reading sequentially a block at a time

Maintain two file pointers While tuple at R < tuple at S, advance R (and vice

versa) While tuples match, output all possible pairings

Maintain a “last in sequence” pointer Preserves sorted order of “outer” relation

Cost: b(R) + b(S) plus sort costs, if necessaryIn practice, approximately linear, 3 (b(R) + b(S))

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Hashing

Several types of hashing: Static hashing Extensible hashing Consistent hashing (used in P2P; we’ll see

later)

Static Hashing

Fixed number of buckets (and pages); overflow when necessary

h(k) mod N = bucket to which data entry with key k belongs

Downside: long overflow chains

h(key) mod N

hkey

Primary bucket pages Overflow pages

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N-1

Extendible Hashing

If a bucket becomes full split in half Use directory of pointers to buckets, double the

directory, splitting just the bucket that overflowed

Directory much smaller than file, so doubling it is much cheaper

Only one page of data entries is split Trick lies in how hash function is adjusted!

Example

Directory is array of size 4. For r’s bucket, take last

‘global depth’ # bits of h(r); we denote r by h(r) If h(r) = 5 = binary 101,

it is in bucket pointed to by 01

Insert: If bucket is full, split it (allocate new page, re-distribute)

If necessary, double directory. (As we will see, splitting a bucket does not always require doubling; we can tell by comparing global depth with local depth for the split bucket.)

13*00

01

10

11

2

2

2

2

2

LOCAL DEPTH

GLOBAL DEPTH

DIRECTORY

Bucket A

Bucket B

Bucket C

Bucket D

DATA PAGES

10*

1* 21*

4* 12* 32* 16*

15* 7* 19*

5*

Insert h(r)=20 (Causes Doubling)

20*

00

01

10

11

2 2

2

2

LOCAL DEPTH 2

2

DIRECTORY

GLOBAL DEPTHBucket A

Bucket B

Bucket C

Bucket D

Bucket A2(`split image'of Bucket A)

1* 5* 21*13*

32*16*

10*

15* 7* 19*

4* 12*

19*

2

2

2

000

001

010

011

100

101

110

111

3

3

3DIRECTORY

Bucket A

Bucket B

Bucket C

Bucket D

Bucket A2(‘split image'of Bucket A)

32*

1* 5* 21*13*

16*

10*

15* 7*

4* 20*12*

LOCAL DEPTH

GLOBAL DEPTH

Points to Note

20 = binary 10100 Last 2 bits (00) r belongs in A or A2 Last 3 bits needed to tell which Global depth of directory: Max # of bits needed to tell

which bucket an entry belongs to Local depth of a bucket: # of bits used to determine if an

entry belongs to this bucket

When does bucket split cause directory doubling? Before insert, local depth of bucket = global depth Insert causes local depth to become > global depth;

directory is doubled by copying it over and `fixing’ pointer to split image page

(Use of least significant bits enables efficient doubling via copying of directory!)

Comments on Extendible Hashing

If directory fits in memory, equality search answered with one disk access; else two Directory grows in spurts, and, if the distribution of hash

values is skewed, directory can grow large Multiple entries with same hash value cause problems!

Delete: If removal of data entry makes bucket empty, can be

merged with ‘split image’ If each directory element points to same bucket as its

split image, can halve directory

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Relevance of Hashing Techniques

Hash indices use extensible hashing Uses of static hashing:

Aggregation Intersection Joins

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Hash Join

Read entire inner relation into hash table (join attributes as key)

For each tuple from outer, look up in hash table & join

Not fully pipelined

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Running out of Memory

Prevention: First partition the data by value into memory-sized groupsPartition both relations in the same way, write to files

Recursively join the partitions

Resolution: Similar, but do when hash tables fullSplit hash table into files along bucket boundaries

Partition remaining data in same wayRecursively join partitions with diff. hash fn!

Hybrid hash join: flush “lazily” a few buckets at a time

Cost: <= 3 * (b(R) + b(S))

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The Duality of Hash and Sort

Different means of partitioning and merging data when comparisons are necessary: Break on physical rule (mem size) in sorting

Merge on logical step, the merge Break on logical rule (hash val) in hashing

Combine using physical step (concat)

When larger-than-memory sorting is necessary, multiple operators use the same key, we can make all operators work on the same in-memory portion of data at the same time

Can we do this with hashing? Hash teams (Graefe)

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What If I Want to Distribute Query Processing?

Where do I put the data in the first place (or do I have a choice)?

How do we get data from point A -> point B?

What about delays? What about “binding patterns”?

Looks kind of like an index join with a sargable predicate

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Pipelined Hash Join Useful for Joining Web Sources

Two hash tables As a tuple comes in,

add to the appropriate side & join with opposite table

Fully pipelined, adaptive to source data rates

Can handle overflow as with hash join

Needs more memory

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The Semi-Join/Dependent Join

Take attributes from left and feed to the right source as input/filter

Important in data integration Simple method:

for each tuple from leftsend to right sourceget data back, join

More complex: Hash “cache” of attributes & mappings Don’t send attribute already seen Bloom joins (use bit-vectors to reduce

traffic)

JoinA.x = B.y

A Bx

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Wrap-Up

Query execution is all about engineering for efficiency O(1) and O(lg n) algorithms wherever possible Avoid looking at or copying data wherever possible Note that larger-than-memory is of paramount

importance Should that be so in today’s world?

As we’ve seen it so far, it’s all about pipelining things through as fast as possible

But may also need to consider other axes: Adaptivity/flexibility – may sometimes need this Information flow – to the optimizer, the runtime system

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Upcoming Readings

For Wednesday: Read Chaudhuri survey as an overview Read and review Selinger et al. paper

For Monday: Read EXODUS and Starburst papers Write one review contrasting the two on the

major issues