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Cornell Talk Notes
2017-09-09 17:41:35 -04:00
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<title>Just-in-Time Data Structures</title>
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Exploring <u><b>O</b></u>nline <u><b>D</b></u>ata <u><b>In</b></u>teractions
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<div class="slides">
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<section>
<!-- Credits... introduce everyone, etc... -->
<section>
<h2>Just-in-Time Data Structures</h2>
<h4>Oliver Kennedy</h4>
<h4><a href="mailto:okennedy@buffalo.edu">okennedy@buffalo.edu</a></h4>
</section>
<section>
<table>
<tr>
<td width="150px"><img src="graphics/saurav.jpg" height="150px"/></td>
<td width="150px"><img src="graphics/darshana.jpg" height="150px"/></td>
<td width="150px"><img src="graphics/hank.jpg" height="150px"/></td>
<td width="150px"><img src="graphics/ankur.jpg" height="150px"/></td>
<td width="150px"><img src="graphics/luke.png" height="150px"/></td>
</tr>
<tr style="font-size: smaller;">
<td>Saurav Singhi</td>
<td>Darshana Balakrishnan<br/</td>
<td>Hank Lin</td>
<td>Ankur Upadhyay</td>
<td>Lukasz Ziarek</td>
</tr>
<tr style="font-size: small;">
<td>(PhD In Progress)</td>
<td>(MS In Progress)</td>
<td>(BS 2017)</td>
<td>(MS 2014)</td>
updates
2017-09-12 20:19:40 -04:00
<td>(Prof @ UB)</td>
Cornell Talk Notes
2017-09-09 17:41:35 -04:00
</tr>
</table>
</section>
</section>
<section>
<!-- Establish the setting:
- Data Structures are a game of trade-offs.
- Which structure is best? Well, it depends!
- Specific data structures lock you in to a specific set of tradeoffs:
- Read vs Write
- Batch vs Individual Updates
- Scan vs Lookup vs Range Queries
-->
updates
2017-09-12 20:19:40 -04:00
<section>
<img src="graphics/conan.png" />
<h3>What is best in life?</h3>
<p class="fragment">(for organizing your data)</p>
<attribution>&copy; Universal Pictures</attribution>
</section>
<section>
<svg width="280" height="500" style="float: right">
<image x="55" y="20" width="180" height="180"
xlink:href="figs/ExampleDSes-BinTree.svg"
/>
<image x="20" y="185" width="250" height="170"
xlink:href="figs/ExampleDSes-LinkedList.svg"
/>
<image x="75" y="290" width="145" height="145"
xlink:href="figs/ExampleDSes-SortedArray.svg"
/>
</svg>
<h3>API</h3>
<ul>
<p>Insert $\lt key, value\gt$</p>
<p>Query for $key \in [low, high)$</p>
</ul>
<hr/>
<h3>Available Structures</h3>
<p>
Binary Tree, Linked List, Sorted Array
</p>
</section>
<section>
<svg width="600" height="600">
<image x="0" y="0" width="600" height="600"
xlink:href="figs/DSTradeoffs.svg"
/>
</svg>
</section>
<section>
<h2>Other Tradeoffs</h2>
<ul>
<li>Support for Threads</li>
<li>Lookup vs Full Scan vs Range Scan</li>
<li>Optimal Update Size</li>
</ul>
</section>
<section>
<svg width="400" height="400" style="float: right">
<image x="0" y="0" width="400" height="400"
xlink:href="figs/DSTradeoffs.svg"
/>
<g class="fragment" data-fragment-index="2">
<g class="fragment fade-out" data-fragment-index="4">
<text x="105" y="97" style="font-weight: bold; fill: red;">[Best]</text>
</g>
</g>
<g class="fragment" data-fragment-index="4">
<g class="fragment fade-out" data-fragment-index="6">
<text x="140" y="224" style="font-weight: bold; fill: red;">[Best]</text>
</g>
</g>
<g class="fragment" data-fragment-index="6">
<g class="fragment fade-out" data-fragment-index="8">
<text x="285" y="280" style="font-weight: bold; fill: red;">[Best]</text>
</g>
</g>
<g class="fragment" data-fragment-index="8">
<text x="95" y="97" style="font-weight: bold; fill: red;">[Best?]</text>
<text x="130" y="224" style="font-weight: bold; fill: red;">[Best?]</text>
</g>
</svg>
<h3>Interactive Analytics</h3>
<ol style="margin-top: 20px;">
<li class="fragment" data-fragment-index="1" style="margin-top: 10px;">User Opens CSV File</li>
<li class="fragment" data-fragment-index="3" style="margin-top: 10px;">User Poses Query as File Loads</li>
<li class="fragment" data-fragment-index="5" style="margin-top: 10px;">Lots More Queries</li>
<li class="fragment" data-fragment-index="7" style="margin-top: 10px;">User Adds More Data</li>
</ol>
<p class="fragment" data-fragment-index="9" style="clear: right; font-weight: bold;">
Even in a single session, there may be more than one "optimal" data structure.
</p>
</section>
Cornell Talk Notes
2017-09-09 17:41:35 -04:00
</section>
<section>
updates
2017-09-12 20:19:40 -04:00
<section>
<h2>State of the Art</h2>
<ul>
<li>Find a jack-of-all-trades data structure</li>
<li>Trash and re-build structures for different workloads</li>
<li>Use a bespoke data structure</li>
</ul>
<p class="fragment" data-fragment-index="1" style="clear: right; font-weight: bold;">
What would it take to enable incremental transitions from one set of tradeoffs to another one?
</p>
<aside class="notes">
<p>1. Jack-of-all-trades, master of none. e.g., B+Tree, LSM Tree</p>
<p>2. a) Expensive, b) Need to be able to predict workload shifts before needed</p>
<p>3. Mountain of programmer effort</p>
</aside>
</section>
<section>
<h2>Incremental Transitions</h2>
<ol>
<li class="fragment">What does it mean for a data structure to be halfway between a Binary Tree and a Linked List?</li>
<li class="fragment">How would we access and manipulate such a data structure?</li>
<li class="fragment">When and how should a data structure transition?</li>
<li class="fragment">How do we automatically generate bespoke data-structures?</li>
</ol>
</section>
<section>
<h2>Incremental Transitions</h2>
<ol>
<li style="color: black;">A Universal Instance Language</li>
<li style="color: grey;">Realizing Universal Data Structures</li>
<li style="color: grey;">Just-In-Time Data Structure Optimization</li>
<li style="color: grey;">Optimization Policy Discovery</li>
</ol>
</section>
Cornell Talk Notes
2017-09-09 17:41:35 -04:00
<!-- Get deeper in to the problem:
- Dynamic workloads: (E.g., Data Loading -> Data access || Regional Differences in Access Patterns)
- State of the art:
- Option 1: Trash the old data structure and build a new one (and you're left twiddling your thumbs while you wait)
- Option 2: Design a data structure *specifically* for your transitional needs (e.g., LSM trees)
- What would it take to allow a data structure to incrementally transition from one set of tradeoffs to another one?
- Challenge: We have no way to work with, or even to describe such an "intermediate" data structure in the middle of transitioning
- Talk outline:
- A Universal Data Structure Instance description language
- Accessing and Modifying Static Data Structures
- Optimizing Static Data Structures
- Dynamic Data
- Policy Discovery and Optimization
-->
</section>
<section>
updates
2017-09-12 20:19:40 -04:00
<section>
<p style="text-align: center">Logical Content</p>
<p style="text-align: center" class="fragment">↑</p>
<p style="text-align: center">Physical Structure</p>
</section>
<section>
<p style="text-align: center">A <i>Bag</i> of $\lt Key \rightarrow Value \gt$ Pairs</p>
<p style="text-align: center">↑</p>
<p style="text-align: center" class="fragment grow">One Physical Realization of the Bag</p>
</section>
<section>
<b>Core Idea</b>: A grammar of physical realizations.
</section>
<section>
<h3>Primitives</h3>
<ul>
<li>A Key ($\mathbb K$)</li>
<li>A Record ($\mathbb R$)<br/>Logically a single record</li>
<li>A Pointer ($\mathbb P$)<br/>Logically a bag of records</li>
</ul>
</section>
<section>
<h3>Grammar</h3>
<p style="text-align: left; width: 300px; margin-left: auto; margin-right: auto; margin-top: 50px">
\begin{align}
\mathbb P :=\; &|\;Sng(\mathbb R) \\
&|\uplus(\mathbb P, \mathbb P) \\
&|\;BT_{\mathbb K}(\mathbb P, \mathbb P) \\
&|\;Array_N(\mathbb R \ldots \mathbb R) \\
&|\;Sorted_N(\mathbb R \ldots \mathbb R)
\end{align}
</p>
</section>
<section>
<h3>Singleton</h3>
<table>
<tr><td style="text-align: right;">Visual:</td><td><img src="figs/singleton.svg" style="margin: 0px;"/></td></tr>
<tr><td style="text-align: right;">UIL:</td><td>$Sng(x: \mathbb R)$</td></tr>
<tr><td style="text-align: right;">Logical:</td><td>$\{ x \}$</td></tr>
</table>
</section>
<section>
<h3>Union Node</h3>
<table>
<tr><td style="text-align: right;">Visual:</td><td><img src="figs/union.svg" style="margin: 0px;"/></td></tr>
<tr><td style="text-align: right;">UIL:</td><td>$\uplus(x: \mathbb P, y: \mathbb P)$</td></tr>
<tr><td style="text-align: right;">Logical:</td><td>$x \uplus y$</td></tr>
</table>
</section>
<section>
<h3>Combining Primitives: Linked List</h3>
<table>
<tr><td style="text-align: right;">Visual:</td><td><img src="figs/linkedlist.svg" style="margin: 0px;"/></td></tr>
<tr><td style="text-align: right;">UIL:</td><td>\begin{align}LL :=\;&|\;U(Sng(x: \mathbb R), y: LL)\\&|\;Sng(x)\end{align}</td></tr>
<tr><td style="text-align: right;">Logical:</td><td>$\{ x \} \uplus y$</td></tr>
</table>
<p class="fragment" data-fragment-index="1" style="clear: right; font-weight: bold;">
Existing data structures can be expressed as syntactic restrictions on this grammar.
</p>
</section>
<section>
<h3>Extension 1: Semantic Constraints</h3>
<table>
<tr><td style="text-align: right;">Visual:</td><td><img src="figs/BTreeNode.svg" style="margin: 0px;"/></td></tr>
<tr><td style="text-align: right;">UIL:</td><td>$BT_{k: \mathbb K}(x: \mathbb P, y: \mathbb P)$</td></tr>
<tr><td style="text-align: right;">Logical:</td><td>$x \uplus y$</td></tr>
<tr><td style="text-align: right;">Constraint:</td><td>$\forall r \in x: r.key \lt K$<br/>$\forall r \in y: r.key \geq K$</td></tr>
</table>
<p class="fragment" data-fragment-index="1" style="clear: right; font-weight: bold;">
Nodes can define syntactic constraints on the contents of descendents.
</p>
</section>
<section>
<h3 style="margin-bottom: 60px;">Combining Primitives: Binary Tree</h3>
\begin{align}
BinTree :=\;&|\;BT_{k: \mathbb K}(x: BinTree, y: BinTree)\\&|\;Sng(x: \mathbb R)
\end{align}
</section>
<section>
<h3>Extension 2: Repetition</h3>
<table>
<tr><td style="text-align: right;">Visual:</td><td><img src="figs/Array.svg" style="margin: 0px;"/></td></tr>
<tr><td style="text-align: right;">UIL:</td><td>$Array_{N : \mathbb N}(x_1: \mathbb R, \ldots, x_N: \mathbb R)$</td></tr>
<tr><td style="text-align: right;">Logical:</td><td>$\{ x_1, \ldots, x_N \}$</td></tr>
</table>
<p class="fragment" data-fragment-index="1" style="clear: right; font-weight: bold;">
Can repeat structures for efficiency (e.g., B+Tree vs BinTree)
</p>
</section>
<section>
<h3>Combining Extensions</h3>
<table>
<tr><td style="text-align: right;">Visual:</td><td><img src="figs/SortedArray.svg" style="margin: 0px;"/></td></tr>
<tr><td style="text-align: right;">UIL:</td><td>$Sorted_{N : \mathbb N}(x_1: \mathbb R, \ldots, x_N: \mathbb R)$</td></tr>
<tr><td style="text-align: right;">Logical:</td><td>$\{ x_1, \ldots, x_N \}$</td></tr>
<tr><td style="text-align: right;">Constraint:</td><td>$\forall i \lt j: x_i.key \leq x_j.key$</td></tr>
</table>
</section>
<section>
<h3>Example</h3>
<svg width="300" height="300">
<image x="0" y="0"
width="300" height="300"
xlink:href="figs/Hybrid.svg"/>
<g>
<polygon points="0,300 150,300 150,218 240,218 240,300 300,300 300,0 0,0" style="fill:white; stroke-width:0" class="fragment fade-out" data-fragment-index="1"/>
<polygon points="0,300 150,300 150,218 200,200 235,120 300,0 0,0" style="fill:white; stroke-width:0" class="fragment fade-out" data-fragment-index="2"/>
<polygon points="0,170 80,170 125,100 150,70 100,0 0,0" style="fill:white; stroke-width:0" class="fragment fade-out" data-fragment-index="3"/>
</g>
</svg>
<p style="font-size: smaller;">
<span class="fragment" data-fragment-index="3">$\uplus(Sng(1), $</span>
<span class="fragment" data-fragment-index="2">$\uplus(Array_2(2,4,7), $</span>
<span class="fragment" data-fragment-index="1">$BT_6($</span>
$Sorted_2(3, 5)$
<span class="fragment" data-fragment-index="1">$, Sng(6))$</span>
<span class="fragment" data-fragment-index="2">$)$</span>
<span class="fragment" data-fragment-index="3">$)$</span>
</p>
</section>
Cornell Talk Notes
2017-09-09 17:41:35 -04:00
<!-- A Universal Data Structure Instance description language
- Initial goal: Describing an instance of a data structure at one specific point in time.
updates
2017-09-12 20:19:40 -04:00
- Definitions:
- Logical vs Physical state (set of records vs the way that those records are laid out on disk)
Cornell Talk Notes
2017-09-09 17:41:35 -04:00
- Approach: Commonalities between different data structures... standard patterns
- Records
- Pointers (to a address of a physical entity that describes a collection of records)
- Semantics (explicit or implicit properties of the physical layout that can improve queries over the ds)
- Specifics: Specific building blocks
- [X] U [Y]
- Record
- Generalizations:
- Repetition (requires array notation)
- Semantic Extensions (Binary Tree, Hash Table, Sorted Array)
- Language (CFG for data structure instances)
- Examples (borrow from paper?)
-->
</section>
<section>
updates
2017-09-12 20:19:40 -04:00
<section>
<h2>Incremental Transitions</h2>
<ol>
<li style="color: grey;">A Universal Instance Language</li>
<li style="color: black;">Realizing Universal Data Structures</li>
<li style="color: grey;">Just-In-Time Data Structure Optimization</li>
<li style="color: grey;">Optimization Policy Discovery</li>
</ol>
</section>
<section>
<h3>Universal Data Structures</h3>
<ul>
<li>Physiological Morphisms<ul>
<li>Queries</li>
<li>Updates</li>
</ul></li>
<li>Purely Physical Morphisms<ul>
<li>Optimization</li>
</ul></li>
</ul>
</section>
<section>
<h3 style="margin-bottom: 60px">Example: Range Queries</h3>
$Q_{\ell,h} : \mathbb P \mapsto \mathbb P$
<p>Return tuples in $[\ell,h)$</p>
</section>
<section style="font-size: smaller">
\begin{align}
Q_{\ell,h}(\uplus(x, y)) \equiv &\;\uplus(Q_{\ell,h}(x), Q_{\ell,h}(y))\\[10px]
Q_{\ell,h}(BT_k(x, y)) \equiv &\;
\begin{cases}
Q_{\ell,h}(x) & \text{if } h \lt k\\
Q_{\ell,h}(y) & \text{if } \ell \geq k\\
BT_k(Q_{\ell,h}(x), Q_{\ell,h}(y)) & \text{otherwise}
\end{cases}\\[10px]
Q_{\ell,h}(Array_N(x_1,\ldots,x_N)) \equiv &\;
Array_{|Y|}(y_1, \ldots, y_{|Y|}) \\&\;\;\text{ s.t. } Y = \{\;x_i\;|\;\ell \leq x_i \lt h\;\}\\[10px]
Q_{\ell,h}(Sorted_N(x_1,\ldots,x_N)) \equiv &\;
Sorted_{j-i+1}(x_i, \ldots, x_j) \\&\;\;\text{ s.t. } i = argmin_i(x_i \geq \ell); \\&\;\;\;\;\;\;\;\;j = argmax_(x_j \lt h);
\end{align}
</section>
<section>
<h3 style="margin-bottom: 60px">Insert</h3>
$$Insert: \mathbb P \times \mathbb P \rightarrow \mathbb P$$
<p style="font-weight: bold; margin-top: 60px" class="fragment">Do the least work possible (optimize later)</p>
<div class="fragment" style="margin-top: 60px">
$$Insert(x, y) \equiv \uplus(x, y)$$
</div>
</section>
Cornell Talk Notes
2017-09-09 17:41:35 -04:00
<!-- Accessing Static Data Structures
- Queries as morphisms on the language
- Lookups
- Scans
updates
2017-09-12 20:19:40 -04:00
- Enumeration via "Pop"
- Implementing "Pop lowest"
Cornell Talk Notes
2017-09-09 17:41:35 -04:00
-->
<!-- Dynamic Data
updates
2017-09-12 20:19:40 -04:00
- Definition: Physical vs logical state transitions: Dynamic data is a physiological transition.
Cornell Talk Notes
2017-09-09 17:41:35 -04:00
- Do the minimum work possible: Linked List
-->
</section>
<section>
updates
2017-09-12 20:19:40 -04:00
<section>
<h2>Incremental Transitions</h2>
<ol>
<li style="color: grey;">A Universal Instance Language</li>
<li style="color: grey;">Realizing Universal Data Structures</li>
<li style="color: black;">Just-In-Time Data Structure Optimization</li>
<li style="color: grey;">Optimization Policy Discovery</li>
</ol>
</section>
Cornell Talk Notes
2017-09-09 17:41:35 -04:00
<!-- Optimizing Static Data Structures
updates
2017-09-12 20:19:40 -04:00
- Now we're talking about purely physical state transitions
Cornell Talk Notes
2017-09-09 17:41:35 -04:00
- Pattern + Replacement Language
- Events
- Examples
- Cracker Index
- Splay Tree
- Lazy BTree
-->
</section>
<section>
updates
2017-09-12 20:19:40 -04:00
<section>
<h2>Incremental Transitions</h2>
<ol>
<li style="color: grey;">A Universal Instance Language</li>
<li style="color: grey;">Realizing Universal Data Structures</li>
<li style="color: grey;">Just-In-Time Data Structure Optimization</li>
<li style="color: black;">Optimization Policy Discovery</li>
</ol>
</section>
<section>
<h1>Policy Discovery</h1>
</section>
Cornell Talk Notes
2017-09-09 17:41:35 -04:00
<!-- Policy Discovery and Optimization
- Purely Heuristic Design: Cracker Index / Transition Policy / Splay Trees
- Assisted Discovery: Parameterized Search Space + Cost Model
- Autonomous Discovery:
- Simulation-Based
- (Likely Expensive) Chase-style
-->
</section>
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