2018-02-19 00:15:53 -05:00
<!doctype html>
< html lang = "en" >
< head >
< meta charset = "utf-8" >
< title > CSE 4/562 - Spring 2018< / title >
< meta name = "description" content = "CSE 4/562 - Spring 2018" >
< meta name = "author" content = "Oliver Kennedy" >
< meta name = "apple-mobile-web-app-capable" content = "yes" / >
< meta name = "apple-mobile-web-app-status-bar-style" content = "black-translucent" / >
< meta name = "viewport" content = "width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no, minimal-ui" >
< link rel = "stylesheet" href = "../reveal.js-3.6.0/css/reveal.css" >
< link rel = "stylesheet" href = "ubodin.css" id = "theme" >
<!-- Code syntax highlighting -->
< link rel = "stylesheet" href = "../reveal.js-3.6.0/lib/css/zenburn.css" >
<!-- Printing and PDF exports -->
< script >
var link = document.createElement( 'link' );
link.rel = 'stylesheet';
link.type = 'text/css';
link.href = window.location.search.match( /print-pdf/gi ) ? '../reveal.js-3.6.0/css/print/pdf.css' : '../reveal.js-3.6.0/css/print/paper.css';
document.getElementsByTagName( 'head' )[0].appendChild( link );
< / script >
< script src = "../reveal.js-3.6.0/lib/js/head.min.js" > < / script >
<!-- [if lt IE 9]>
< script src = "../reveal.js-3.6.0/lib/js/html5shiv.js" > < / script >
<![endif]-->
< / head >
< body >
< div class = "reveal" >
<!-- Any section element inside of this container is displayed as a slide -->
< div class = "header" >
<!-- Any Talk - Specific Header Content Goes Here -->
CSE 4/562 - Database Systems
< / div >
< div class = "slides" >
2018-02-26 00:30:14 -05:00
<!-- 2018 by OK:
Indexing really belongs *before* we discuss join algorithms.
Not only is indexing fundamental to several joins (1-pass, 2-pass, INLJ), but it
organizes the discussion of algorithms in a more contiguous block.
-->
2018-02-19 00:15:53 -05:00
< section >
< h1 > Indexes< / h1 >
< h3 > CSE 4/562 – < / h3 >
< h5 > February 19, 2018< / h5 >
< / section >
< section >
< section >
< table >
< tr >
< td >
< img src = "graphics/Books/DBSystemsHardcover.jpg" height = "200px" >
< / td >
< td >
< img src = "graphics/Books/DBSystemsSoftcover.jpg" height = "200px" >
< / td >
< / tr >
< tr class = "fragment" >
< td > $150< / td >
< td > $50< / td >
< / tr >
< tr class = "fragment" >
< td > Index< br / > ToC< / td >
< td > No Index< br / > ToC Summary< / td >
< / tr >
< / table >
< / section >
< section >
< h3 > Today's Focus< / h3 >
< p style = "margin: 100px;" >
$\sigma_C(R)$ < span style = "margin: 50px" > and< / span > $(\ldots \bowtie_C R)$
< / p >
< p class = "fragment" style = "font-size: 70%" > (Finding records in a table < span class = "fragment" > really fast< / span > )< / p >
< / section >
< section >
< h3 > Indexing Strategies< / h3 >
< dl >
< div class = "fragment" >
< dt > Rearrange the data.< / dt >
< dd > Put things in a predictable location or a specific order.< / dd >
< dd class = "fragment" > ("clustering" the data)< / dd >
< / div >
< div class = "fragment" >
< dt > Wrap the data.< / dt >
< dd > Record where specific data values live< / dd >
< dd class = "fragment" > ("indexing" the data).< / dd >
< / div >
< / dl >
< / section >
< section >
< h3 > Data Organization< / h3 >
< dl >
< div class = "fragment" >
< dt > Unordered Heap< / dt >
< dd > No organization at all. $O(N)$ reads.< / dd >
< / div >
< div class = "fragment" >
< dt > (Secondary) Index< / dt >
< dd > Index structure over unorganized data. $O(\ll N)$ < b > random< / b > reads for < b > some< / b > queries.< / dd >
< / div >
< div class = "fragment" >
< dt > Clustered (Primary) Index< / dt >
< dd > Index structure over clustered data. $O(\ll N)$ < b > sequential< / b > reads for < b > some< / b > queries.< / dd >
< / div >
< / dl >
< / section >
< section >
< h3 > Data Organization< / h3 >
< img src = "graphics/2018-02-19-Index-Types.svg" / >
< / section >
< section >
< h3 > Data Organization< / h3 >
< img src = "graphics/2018-02-19-PrimaryVsSecondary.png" / >
< / section >
< section >
< h3 > Index Types< / h3 >
< dl >
< dt > Tree-Based< / dt >
< dd > A hierarchy of decisions lead to data at the leaves.< / dd >
< div class = "fragment highlight-grey" data-fragment-index = 2 >
< dt > Hash-Based< / dt >
< dd > A hash function puts data in predictable locations.< / dd >
< dt > CDF-Based < span style = "color: red" class = "fragment" data-fragment-index = 1 > (new)< / span > < / dt >
< dd > A more complex function predicts where data lives.< / dd >
< / div >
< / dl >
< / section >
< / section >
< section >
< section >
< h3 > Tree-Based Indexes< / h3 >
< svg data-src = "graphics/2018-02-19-Tree-BinSearch.svg" / >
< / section >
< section >
< h3 > Tree-Based Indexes< / h3 >
< svg data-src = "graphics/2018-02-19-Tree-Motivation.svg" / >
< / section >
< section >
< h3 > Challenges< / h3 >
< dl >
< dt > Balance< / dt >
< dd > Bad question orders lead to poor performance!< / dd >
< dt > IO< / dt >
< dd > Each access to a binary tree node is a random access.< / dd >
< dt class = "fragment highlight-grey" data-fragment-index = "1" > Which Dimension< / dt >
< dd class = "fragment highlight-grey" data-fragment-index = "1" > Why limit ourselves to asking about one dimension?< / dd >
< / dl >
< / section >
< section >
< svg data-src = "graphics/2018-02-19-Tree-Unbalanced.svg" class = "stretch" / >
< / section >
< section >
< h3 > Worst-Case Tree?< / h3 >
< div class = "fragment" style = "margin: 100px" > $O(N)$ with the tree laid out left/right-deep< / div >
< h3 class = "fragment" > Best-Case Tree?< / h3 >
< div class = "fragment" style = "margin: 100px" > $O(\log N)$ with the tree perfectly balanced< / div >
< / section >
< / section >
< section >
< section >
< h3 > Binary Trees are Bad for IO< / h3 >
< p style = "margin-top: 100px;" > Every step of binary search is a random access< / p >
< p style = "margin-top: 100px;" class = "fragment" > Every tree node access is a random access< / p >
< / section >
< section >
< p > Random access IO is bad.< / p >
< / section >
< section >
< p > < b > Idea: < / b > Load a bunch of binary tree nodes together.< / p >
< / section >
< section >
< p > < b > Binary Tree: < / b > $1$ separator & $2$ pointers< / p >
< p > $log_2(N)$ Deep< / p >
< p class = "fragment" data-fragment-index = "1" style = "margin-top: 50px;" > < b > $K$-ary Tree: < / b > $(K-1)$ separators & $K$ pointers< / p >
< p class = "fragment" data-fragment-index = "1" > $log_K(N)$ Deep< / p >
< / section >
< section >
< p > < b > Important:< / b > You still need to do binary search on each node of a $K$-ary tree, but now you're doing random access on memory (or cache) instead of disk (or memory)< / p >
< / section >
< section >
< h3 > ISAM Trees< / h3 >
< img src = "graphics/2018-02-19-ISAM.png" height = "500px" >
< / section >
< / section >
< section >
< section >
< p > How do you handle updates?< / p >
< p style = "margin-top: 50px;" class = "fragment" > B+Tree = ISAM + Updates< / p >
< / section >
< section >
< h3 > Challenges< / h3 >
< ul >
< li class = "fragment" > Finding space for new records< / li >
< li class = "fragment" > Keeping the tree balanced as new records are added< / li >
< / ul >
< / section >
< section >
< p > < b > Idea 1:< / b > Reserve space for new records< / p >
< / section >
< section >
< svg data-src = "graphics/2018-02-19-BTree-Reserved.svg" / >
< / section >
< section >
< p > Just maintaining open space won't work forever...< / p >
< / section >
< section >
< h3 > Rules of B+Trees< / h3 >
< dl >
< dt > Keep space open for insertions in inner/data nodes.< / dt >
< dd > ‘ ’ ’ < / dd >
< dt > Avoid under-using space< / dt >
< dd > ‘ ’ ’ < / dd >
< / dl >
< p class = "fragment" > < b > Maintain Invariant:< / b > All Nodes ≥ 50% Full< / p >
< p class = "fragment" > (Exception: The Root)< / p >
< / section >
< / section >
< section >
< section > < img src = "graphics/2018-02-19-InsertExample-1.png" height = "300px" / > < / section >
< section > < img src = "graphics/2018-02-19-InsertExample-2.png" height = "300px" / > < / section >
< section > < img src = "graphics/2018-02-19-InsertExample-3.png" height = "300px" / > < / section >
< section > < img src = "graphics/2018-02-19-InsertExample-4.png" height = "300px" / > < / section >
< section > < img src = "graphics/2018-02-19-InsertExample-5.png" height = "300px" / > < / section >
< section > < img src = "graphics/2018-02-19-InsertExample-6.png" height = "300px" / > < / section >
< section > < img src = "graphics/2018-02-19-InsertExample-7.png" height = "300px" / > < / section >
< section > < img src = "graphics/2018-02-19-InsertExample-8.png" height = "300px" / > < / section >
< section > < p > Deletions reverse this process (at 50% fill).< / p > < / section >
< / section >
2018-02-22 20:52:52 -05:00
< section >
< a href = "https://www.cs.usfca.edu/~galles/visualization/BPlusTree.html" style = "font-size: 200%; font-weight: bold;" > Demo< / a >
< / section >
2018-02-19 00:15:53 -05:00
< section >
< p > < b > Next Class< / b > : Hash- and CDF-Based Indexes< / p >
< / section >
< / div > < / div >
< script src = "../reveal.js-3.6.0/js/reveal.js" > < / script >
< script >
// Full list of configuration options available at:
// https://github.com/hakimel/../reveal.js#configuration
Reveal.initialize({
2018-02-26 19:44:30 -05:00
controls: true,
2018-02-19 00:15:53 -05:00
progress: true,
history: true,
center: true,
slideNumber: true,
transition: 'fade', // none/fade/slide/convex/concave/zoom
chart: {
defaults: {
global: {
title: { fontColor: "#333", fontSize: 24 },
legend: {
labels: { fontColor: "#333", fontSize: 20 },
},
responsiveness: true
},
scale: {
scaleLabel: { fontColor: "#333", fontSize: 20 },
gridLines: { color: "#333", zeroLineColor: "#333" },
ticks: { fontColor: "#333", fontSize: 16 },
}
},
line: { borderColor: [ "rgba(20,220,220,.8)" , "rgba(220,120,120,.8)", "rgba(20,120,220,.8)" ], "borderDash": [ [5,10], [0,0] ]},
bar: { backgroundColor: [
"rgba(220,220,220,0.8)",
"rgba(151,187,205,0.8)",
"rgba(205,151,187,0.8)",
"rgba(187,205,151,0.8)"
]
},
pie: { backgroundColor: [ ["rgba(0,0,0,.8)" , "rgba(220,20,20,.8)", "rgba(20,220,20,.8)", "rgba(220,220,20,.8)", "rgba(20,20,220,.8)"] ]},
radar: { borderColor: [ "rgba(20,220,220,.8)" , "rgba(220,120,120,.8)", "rgba(20,120,220,.8)" ]},
},
// Optional ../reveal.js plugins
dependencies: [
{ src: '../reveal.js-3.6.0/lib/js/classList.js', condition: function() { return !document.body.classList; } },
{ src: '../reveal.js-3.6.0/plugin/math/math.js',
condition: function() { return true; },
mathjax: '../reveal.js-3.6.0/js/MathJax.js'
},
{ src: '../reveal.js-3.6.0/plugin/markdown/marked.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
{ src: '../reveal.js-3.6.0/plugin/markdown/markdown.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
{ src: '../reveal.js-3.6.0/plugin/highlight/highlight.js', async: true, condition: function() { return !!document.querySelector( 'pre code' ); }, callback: function() { hljs.initHighlightingOnLoad(); } },
{ src: '../reveal.js-3.6.0/plugin/zoom-js/zoom.js', async: true },
{ src: '../reveal.js-3.6.0/plugin/notes/notes.js', async: true },
// Chart.min.js
{ src: '../reveal.js-3.6.0/plugin/chart/Chart.min.js'},
// the plugin
{ src: '../reveal.js-3.6.0/plugin/chart/csv2chart.js'},
{ src: '../reveal.js-3.6.0/plugin/svginline/es6-promise.auto.js', async: false },
{ src: '../reveal.js-3.6.0/plugin/svginline/data-src-svg.js', async: false }
]
});
< / script >
< / body >
< / html >
