March, 2002

Efficient Bitmap Indexing Techniques for Very Large Datasets

Kesheng John WuEkow Otoo

Arie Shoshani

March, 2002

Problem Statement

• Main objective: maps logical requests to qualified objects— A logical request:

• 20001015<=eventTime & 200<energy<300 …— Objects:

• Set of object ids; • Set of files containing the objects; • Offsets within the files, …

March, 2002

Application: STAROID dst hist mEvent

NumbermEventTime

mRunNumber

NLb

0 159625 159627 2635 20000827.011759

1239029 1341

1 159625 159627 2636 20000827.011759

1239029 1470

2 159625 159627 2637 20000827.011759

1239029 1663

OID n_clus_tpc_in[13]

numberOfPrimaryTracks

ChargedParticles_Means[1]

PrimaryVertexX

qxb[2] zdc2Energy

0 909 1228 266 .56 -26.40 48

1 1243 1415 317 .46 -29.08 53

2 1285 1533 281 .53 -6.754 8

A portion of the STAR tag dataset: 3 events with 12 attributes from millions of events with 502 attributes.

March, 2002

Application: Combustion

• Direct numerical simulation of auto-ignition process (solution of complex partial differential equations)

• A dozen or more variables are computed at each time step and each grid point

• Number of grid points: 2D 600 X 600 >>> 3D 1000 X 1000 X 1000

• Time steps: 100 >>> 1000s• Data size: 1 GB >>> 10 TB• Task: identify features and track them across

time steps• E.G. Find flame front across time

Find “600<temp<700” for 1 billion points per time step, and discover overlap between time steps

• Use compressed bitmaps to accelerate both feature extraction and feature tracking 1000 X 1000 X 1000

March, 2002

Building a Bitmap Index

1. Partition each property into bins (binning)— e.g. for 0<NLb<4000, 20 equal size bins: [0, 200)[200,400)…

2. Generate a bit vector for each bin (encoding)— Bit i of bit vector j is 1 iff NLb[i] is in bin j

3. Compress each bit vector

000000000000000

000010001000000

000001110111011

101100000000000

010000000000000

000000000000100

000000000000000

property 1

000001110111011

101100000000000

010000001000000

000000000000100

000000000000000

property 2

000000000000000

000000001000000

000001110111011

101100000000000

010000000000000

000000000000100

000000000000000

property n

000010000000000

. . .

March, 2002

Advantages of Bitmap Index

• Bitmap index: specialized index that takes advantage— Read-mostly data: data produced from scientific

experiments can be appended in large groups• Fast operations

— “Predicate queries” can be performed with bitwise logical operations• Predicate ops: =, <, >, <=, >=, range,• Logical ops: AND, OR, XOR, NOT

— They are well supported by hardware• Easy to compress, potentially small index size• Each individual bitmap is small and frequently used ones

can be cached in memory

March, 2002

Operation-efficient Compression Methods

• Best known: byte-aligned bitmap code (BBC)— Uses run-length encoding (next slide)— Byte alignment, optimized for space efficiency— Decoding on bit level, not optimal for operations— Used in oracle

• We developed a new word-aligned scheme: WAH— Uses run-length encoding— Word alignment— Designed for minimal decoding to gain speed

March, 2002

Operation-efficient Compression Methods

Uncompressed:0000000000001111000000000 ......0000001000000001111111100000000 .... 000000

Compressed:12, 4, 1000,1,8,1000

Store very short sequences as-is

Advantage:

Can perform: AND, OR, COUNT operations on compressed data

Based on variations of Run Length Compression

March, 2002

Trade-off of Compression Schemes

uncompressedWAH

space

speed

better

gzip

BBC

ExpGolPacBits

March, 2002

Information About the Test Machines

• Hardware and system— Sun enterprise 450 (Ultrasparc II 400mhz)— 4GB RAM— VARITAS volume manager (stripped disk)

• Real application data from STAR— Above 2 million objects, 12 attributes

• Synthetic data— 100 million objects, 10 attributes

• Terms— Compression ratio: ratio of compressed bitmaps

size and uncompressed bitmaps size — Time reported are wall clock time in seconds

March, 2002

Logical Operation Time(Synthetic Data) 10X improvement

March, 2002

Logical Operation Time (STAR Data)Also 10X improvement

March, 2002

Encoding Schemes – Main Idea

Equalityencoding

Rangeencoding

Intervalencoding

12 bins 1 2 3 4 5 6 7 8 9 10 11 12

Interval, Range encoding: operates on 2 bins only!

March, 2002

Total Effect of Compression and Encoding Schemes

• Bottom line on queries— Compression scheme determines efficiency of

logical operations— Encoding scheme determines number of operations

• Range & interval – only one logical operation over 2 bitmaps

• Equality – many operations depending on number of bins— But, space may be a consideration

• What is the trade-off?

March, 2002

Interval Encoding Is Better Overall(WAH Compression)

Points on the graphs represent:10, 20, 30, 50, 100Bins.

Average time for random range queries

March, 2002

Timing Results

Method Index(X data)

Time (sec)

Speed

ORACLE Scan 0 6 0.1

B-tree 3.6 0.95 0.6

Native vertical partition

Scan 0 0.57 1

20 bins 0.18 0.11 5

50 bins 0.43 0.07 8

100 bins 0.90 0.05 11

March, 2002

Summary

• Compressed bitmap indices are effective for range queries

• Better compression scheme— 50% more space, but 12 time faster !!!

• Among the different encoding schemes— The interval encoding is the overall winner

March, 2002

Future Work

• Support NULL value and categorical values• On-line update: add new data and update index

without interrupting request processing• Recovery mechanism for robustness• Potential new applications: climate, astrophysics,

biology (microarrays)• Study non-uniform binning strategies• Study more encoding schemes• Integrate with conventional database system: to better

handle metadata, to provide more versatile front-end

March, 2002

How Many Bins for Continuous Domains?

Range(x)R

ange

(y)

Edge binEdge bin

.. ... ... ... ... ... .

.. ... ... ... ... ... ... ... ... ... .

.. ... .More bins

Less objects in edge bins

Searching edge bins: skip-scan over “attribute vertical partition”