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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML>
<HEAD>
<META HTTP-EQUIV="CONTENT-TYPE" CONTENT="text/html; charset=utf-8">
<TITLE></TITLE>
<META NAME="GENERATOR" CONTENT="LibreOffice 3.5 (Linux)">
<META NAME="CREATED" CONTENT="20130201;15194200">
<META NAME="CHANGED" CONTENT="20130308;13572500">
<STYLE TYPE="text/css">
<!--
@page { margin: 2cm }
P { margin-bottom: 0.21cm }
TD P { margin-bottom: 0cm }
A:link { so-language: zxx }
-->
</STYLE>
</HEAD>
<BODY LANG="en-US" DIR="LTR">
<P STYLE="margin-bottom: 0cm"><B>Bitmap-Index and Typology</B></P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm"><A NAME="result_box1"></A><A NAME="result_box2"></A>
<SPAN LANG="en-US">This is a C++11 reimplementation of the
<A HREF="http://typology.de/">http://typology.de/</A> idea using
bitmap-indexes. The original approach is written in Java and uses
multidimensional index trees. The aim of this reimplementation is a
prove of concept that bitmaps are suitable for that kind of task. In
my first experiments this program was approximately 10 times faster
than the original. </SPAN>
</P>
<P STYLE="margin-bottom: 0cm">A test import of 96,588,320 german
source-target-score triples results in 28,405 files with a total size
of 6.7 GB. This includes bitmap-indexes up to the fifth character of
the target-word and a source-word look-up table.</P>
<P STYLE="margin-bottom: 0cm">On my notebook (Intel quad core i5 2.67
GHz, 8 GB RAM, 256 GB SSD) one next word prediction takes 0,6 ms in
average. After 2 million requests the memory mapped file “cache”
is hot and the average time goes down to 0.1 ms. When all files were
loaded in the main memory I observed response times of 0.05 ms.</P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm">The query for next word prediction in
SQL:</P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<OL>
<LI><P STYLE="margin-bottom: 0cm">SELECT target, score FROM typology
WHERE source = 'die' AND target like '<SPAN STYLE="background: #ffff00">%</SPAN>'
ORDER BY score DESC LIMIT 10;</P>
<LI><P STYLE="margin-bottom: 0cm">SELECT target, score FROM typology
WHERE source = 'die' AND target like '<SPAN STYLE="background: #ffff00">a%</SPAN>'
ORDER BY score DESC LIMIT 10;</P>
<LI><P STYLE="margin-bottom: 0cm">SELECT target, score FROM typology
WHERE source = 'die' AND target like '<SPAN STYLE="background: #ffff00">ab%</SPAN>'
ORDER BY score DESC LIMIT 10;</P>
<LI><P STYLE="margin-bottom: 0cm">SELECT target, score FROM typology
WHERE source = 'die' AND target like '<SPAN STYLE="background: #ffff00">abc%</SPAN>'
ORDER BY score DESC LIMIT 10;</P>
</OL>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm">Preprocessing step in SQL:</P>
<P STYLE="margin-bottom: 0cm">source, target, score = SELECT source,
target, score FROM typology GROUP BY source, target, score ORDER BY
score DESC;</P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<TABLE WIDTH=219 CELLPADDING=4 CELLSPACING=0>
<COL WIDTH=72>
<COL WIDTH=63>
<COL WIDTH=58>
<TR VALIGN=TOP>
<TD WIDTH=72 STYLE="border-top: 1px solid #000000; border-bottom: none; border-left: 1px solid #000000; border-right: none; padding-top: 0.1cm; padding-bottom: 0cm; padding-left: 0.1cm; padding-right: 0cm">
<P><B>source</B></P>
</TD>
<TD WIDTH=63 STYLE="border-top: 1px solid #000000; border-bottom: none; border-left: 1px solid #000000; border-right: none; padding-top: 0.1cm; padding-bottom: 0cm; padding-left: 0.1cm; padding-right: 0cm">
<P><B>target</B></P>
</TD>
<TD WIDTH=58 STYLE="border-top: 1px solid #000000; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding-top: 0.1cm; padding-bottom: 0cm; padding-left: 0.1cm; padding-right: 0.1cm">
<P><B>score</B></P>
</TD>
</TR>
<TR VALIGN=TOP>
<TD WIDTH=72 STYLE="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0cm; padding-left: 0.1cm; padding-right: 0cm">
<P>das</P>
</TD>
<TD WIDTH=63 STYLE="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0cm; padding-left: 0.1cm; padding-right: 0cm">
<P STYLE="font-weight: normal">zba</P>
</TD>
<TD WIDTH=58 STYLE="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0cm 0.1cm">
<P>0.6</P>
</TD>
</TR>
<TR VALIGN=TOP>
<TD WIDTH=72 STYLE="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0cm; padding-left: 0.1cm; padding-right: 0cm">
<P>die</P>
</TD>
<TD WIDTH=63 STYLE="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0cm; padding-left: 0.1cm; padding-right: 0cm">
<P STYLE="font-weight: normal">aba</P>
</TD>
<TD WIDTH=58 STYLE="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0cm 0.1cm">
<P>0.81</P>
</TD>
</TR>
<TR VALIGN=TOP>
<TD WIDTH=72 STYLE="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0cm; padding-left: 0.1cm; padding-right: 0cm">
<P>die</P>
</TD>
<TD WIDTH=63 STYLE="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0cm; padding-left: 0.1cm; padding-right: 0cm">
<P STYLE="font-weight: normal">aab</P>
</TD>
<TD WIDTH=58 STYLE="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0cm 0.1cm">
<P>0.80</P>
</TD>
</TR>
<TR VALIGN=TOP>
<TD WIDTH=72 STYLE="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0cm; padding-left: 0.1cm; padding-right: 0cm">
<P>die</P>
</TD>
<TD WIDTH=63 STYLE="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0cm; padding-left: 0.1cm; padding-right: 0cm">
<P STYLE="font-weight: normal">cac</P>
</TD>
<TD WIDTH=58 STYLE="border-top: none; border-bottom: none; border-left: 1px solid #000000; border-right: 1px solid #000000; padding: 0cm 0.1cm">
<P>0.56</P>
</TD>
</TR>
<TR VALIGN=TOP>
<TD WIDTH=72 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>du</P>
</TD>
<TD WIDTH=63 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P STYLE="font-weight: normal">cb</P>
</TD>
<TD WIDTH=58 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm">
<P>0.99</P>
</TD>
</TR>
</TABLE>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm"><A NAME="result_box"></A><A NAME="result_box3"></A>
Generate for each letter of <B>target</B> a bitmap-index. TODO:
figure out how much character need their own index. In my experiments
only the first 5 character were indexed. <SPAN LANG="en">Probably,
the first three are sufficient.</SPAN></P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<TABLE WIDTH=654 CELLPADDING=4 CELLSPACING=0>
<COL WIDTH=91>
<COL WIDTH=92>
<COL WIDTH=22>
<COL WIDTH=21>
<COL WIDTH=22>
<COL WIDTH=21>
<COL WIDTH=22>
<COL WIDTH=22>
<COL WIDTH=21>
<COL WIDTH=22>
<COL WIDTH=21>
<COL WIDTH=22>
<COL WIDTH=22>
<COL WIDTH=21>
<COL WIDTH=22>
<COL WIDTH=64>
<TR VALIGN=TOP>
<TD ROWSPAN=2 WIDTH=91 HEIGHT=21 STYLE="border-top: 1px solid #000000; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0.1cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>row number</P>
</TD>
<TD ROWSPAN=2 WIDTH=92 STYLE="border-top: 1px solid #000000; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0.1cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P><B>source<BR></B><SPAN STYLE="font-weight: normal">string</SPAN></P>
<P><BR>
</P>
</TD>
<TD COLSPAN=4 WIDTH=109 STYLE="border-top: 1px solid #000000; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0.1cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P><B>first_letter</B></P>
</TD>
<TD COLSPAN=4 WIDTH=110 STYLE="border-top: 1px solid #000000; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0.1cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P><B>second_letter</B></P>
</TD>
<TD COLSPAN=4 WIDTH=109 STYLE="border-top: 1px solid #000000; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0.1cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P><B>third_letter</B></P>
</TD>
<TD WIDTH=22 STYLE="border-top: 1px solid #000000; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0.1cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>...</P>
</TD>
<TD ROWSPAN=2 WIDTH=64 STYLE="border: 1px solid #000000; padding: 0.1cm">
<P><B>score</B> float</P>
<P>(pre-orderd)</P>
</TD>
</TR>
<TR VALIGN=TOP>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>a</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>b</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>c</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>z</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>a</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>b</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>c</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>z</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>a</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>b</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>c</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>z</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>...</P>
</TD>
</TR>
<TR VALIGN=TOP>
<TD WIDTH=91 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=92 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>das</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>…</P>
</TD>
<TD WIDTH=64 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm">
<P>0.6</P>
</TD>
</TR>
<TR VALIGN=TOP>
<TD WIDTH=91 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=92 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>die</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>…</P>
</TD>
<TD WIDTH=64 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm">
<P>0.81</P>
</TD>
</TR>
<TR VALIGN=TOP>
<TD WIDTH=91 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>2</P>
</TD>
<TD WIDTH=92 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>die</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>…</P>
</TD>
<TD WIDTH=64 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm">
<P>0.80</P>
</TD>
</TR>
<TR VALIGN=TOP>
<TD WIDTH=91 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>3</P>
</TD>
<TD WIDTH=92 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>die</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>…</P>
</TD>
<TD WIDTH=64 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm">
<P>0.56</P>
</TD>
</TR>
<TR VALIGN=TOP>
<TD WIDTH=91 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>4</P>
</TD>
<TD WIDTH=92 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>du</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>1</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=21 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>0</P>
</TD>
<TD WIDTH=22 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: none; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0cm">
<P>…</P>
</TD>
<TD WIDTH=64 STYLE="border-top: none; border-bottom: 1px solid #000000; border-left: 1px solid #000000; border-right: 1px solid #000000; padding-top: 0cm; padding-bottom: 0.1cm; padding-left: 0.1cm; padding-right: 0.1cm">
<P>0.99</P>
</TD>
</TR>
</TABLE>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm">For a fast random access create a hash
index on <B>source and the row numbers </B><SPAN STYLE="font-weight: normal">corresponding
to the source. For the example above a key value pair would looks
like (key = 'die', value = [1,3]).</SPAN></P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<P STYLE="margin-bottom: 0cm">Query with bitmap-indexes:</P>
<P STYLE="margin-bottom: 0cm"><BR>
</P>
<OL>
<LI VALUE=1><P STYLE="margin-bottom: 0cm">SELECT target, score FROM
typology WHERE source = 'die' ORDER BY score DESC LIMIT 10;</P>
<LI><P STYLE="margin-bottom: 0cm">SELECT target, score FROM typology
WHERE source = 'die' AND <SPAN STYLE="background: #ffff00">first_letter
= 'a'</SPAN> ORDER BY score DESC LIMIT 10;</P>
<LI><P STYLE="margin-bottom: 0cm">SELECT target, score FROM typology
WHERE source = 'die' AND <SPAN STYLE="background: #ffff00">first_letter
= 'a' AND second_letter = 'b'</SPAN> ORDER BY score DESC LIMIT 10;</P>
<LI><P STYLE="margin-bottom: 0cm">SELECT target, score FROM typology
WHERE source = 'die' AND <SPAN STYLE="background: #ffff00">first_letter
= 'a' AND second_letter = 'b' AND third_letter = 'c' </SPAN> ORDER
BY score DESC LIMIT 10;</P>
</OL>
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