Providing Practical Software Solutions

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Specialized Indexing

Jim Klucar

jlklucar@praxiseng.com

Accumulo Meetup

10/16/2012

Accumulo Sorts Key/Value Pairs

Data is retrieved by iterating over ranges of keys

Integers: 1, 11, 2

Floats: 2.3e4, 2.3e-4

Multi-dimensional data (-76.76, 39.12)??

Overview

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Zero-Pad Integers to maintain sort order

001

002

003

Reverse sort order by subtracting from

larger number before using integer

(1000 - 003) = 997

(1000 - 002) = 998

(1000 - 001) = 999

Integer Indexing

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Accumulo uses reverse technique on timestamp to have most recent keys sort first

Binary Representation

[sign] [exponent] [mantissa]

If sign bit is set, Flip all bits

If sign bit isn’t set, flip just sign bit

Flipping bits is safely done with XOR

If sign bit is set, XOR with 0xFFFFFFFF

If sign not set, XOR with 0x80000000

IEEE-754 Floating Point Indexing

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Note: Exponent is biased, not 2’s complement

Same procedure can be performed for base 10

numbers with caveats:

Adjust mantissa and exponent so decimal point is at the

same location (32.4e010 -> 3.24e009)

Apply same logic to exponent

Move both signs to first characters

Flipping a bit is subtracting digit from 9

-3.24e-9 becomes ++6.7500000e990

Be sure to print enough digits

Single (32-bit) 8 decimal digits, 3 exponent

Double(64-bit) 15 decimal digits, 4 exponent

Quad (128-bit) 35 decimal digits, 5 exponent

But Binary is so 1970’s…

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Encoding Multi-Dimensional Data

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http://xkcd.com/426/

Sorted Key/Value tables are 1 dimensional

Keys are either greater than or less than each

other

Need a method to map higher dimensional

data (eg 2-D,Lon/Lat) to a lower dimension

Maintain locality of higher dimensional

data in lower dimensional space

Maintain 2D query performance

The Problem

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Concatenate Latitude and Longitude

Bad Idea! Must search entire range of one

dimension to find results

Solution 1

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Solution 2: Z-Ordering

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http://en.wikipedia.org/wiki/Z-order_curve

1 2

3 4

1 2

3 4

5 6

7 8

Easiest of Space-filling curves

Implemented by interleaving digits

from alternating dimensions

Lon -76.8 Lat 35.4

-+736584

Range Search with Z-order

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Must filter out results that aren’t actually inside range ( Accumulo Iterator! )

Avoids full table scan / one dimension scan

Find z-ordering of two corners of search box. Scan from 1 to the other.

Z-Order on Lon / Lat

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How Many Digits of Latitude?

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39.123092 690 Miles

69 Miles

6.9 Miles

1200 Yards

120 Yards

36 Feet

3.6 Feet

4 inches

Developed for http://geohash.org

Concatenating Lon/Lat in a URL is patented!

A geohash defines an area from successive

bisections of areas of the earth.

Longitude Example:

Solution 3: Geohash

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Longitude Geohash Example

14 Bisect the earth, choose which side of bisection point lies on,

use that bit as first bit for longitude geocode ( 1 in this case )

1 0

Longitude Geohash Example

15 Bisect section containing point, rinse repeat.

Code is now: 10

1 0

Longitude Geohash Example

16 Bisect section containing point, rinse repeat.

Code is now: 101

1 0

Perform same operation with latitude.

This defines a box around the point to

arbitrary precision.

Point of interest is in a box, not in the

center of the box

Bits are interleaved Longitude first, then

base-32 encoded

( 57.64911,10.40744) = u4ruydqqvj

Final geocode

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See Wikipedia for worked example

http://en.wikipedia.org/wiki/Geohash

Google Earth KML Demo

http://api.prezzibenzina.it/geohash.kml

Google Earth Visualization

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Range Search Can Be The Same

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Performance difference varies by location and search area

Can calculate geohashes of surrounding

areas of a point deterministically

Search those areas independently

Range / Area Search Alternative

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dqcqzkd

dqcrp dqcqn

dqcqy dqcwb

dqcqx

dqcx0

dqcw8 dqcqw

Point: dqcqzkd

Find parent geohash: dqc

Find neighbor hashes:

dqcqn,dqcrp, etc

Get search ranges

dqcqn00 - dqcqnzz

dqcrp00 – dqcrpzz

…etc

Crank up a batch scanner

Search Expands From Center

Outward

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Geohashes are areas, z-order lon/lat are

points

Geohash is in public domain

Geohash can more easily proximity search

Key Differences

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Watch border regions in range searches

Across equator

Across prime meridian

On top of poles

Across base-32 encoding edges

What to watch

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