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|
||||
|
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3
slides/talks/2017-4-Cornell-JITDs/figs/SortedArray.svg
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3
slides/talks/2017-4-Cornell-JITDs/figs/SortedArray.svg
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|
|
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|
|||
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|
||||
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
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|
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3
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slides/talks/2017-4-Cornell-JITDs/figs/Union.svg
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|
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|
||||
|
After Width: | Height: | Size: 4.9 KiB |
BIN
slides/talks/2017-4-Cornell-JITDs/graphics/conan.png
Normal file
BIN
slides/talks/2017-4-Cornell-JITDs/graphics/conan.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 242 KiB |
|
|
@ -100,7 +100,7 @@
|
|||
<td>(MS In Progress)</td>
|
||||
<td>(BS 2017)</td>
|
||||
<td>(MS 2014)</td>
|
||||
<td>(Asst. Prof @ UB)</td>
|
||||
<td>(Prof @ UB)</td>
|
||||
</tr>
|
||||
</table>
|
||||
</section>
|
||||
|
|
@ -115,9 +115,130 @@
|
|||
- Batch vs Individual Updates
|
||||
- Scan vs Lookup vs Range Queries
|
||||
-->
|
||||
|
||||
<section>
|
||||
<img src="graphics/conan.png" />
|
||||
|
||||
<h3>What is best in life?</h3>
|
||||
<p class="fragment">(for organizing your data)</p>
|
||||
|
||||
<attribution>© 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>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<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>
|
||||
<!-- Get deeper in to the problem:
|
||||
- Dynamic workloads: (E.g., Data Loading -> Data access || Regional Differences in Access Patterns)
|
||||
- State of the art:
|
||||
|
|
@ -135,8 +256,142 @@
|
|||
</section>
|
||||
|
||||
<section>
|
||||
<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>
|
||||
|
||||
<!-- A Universal Data Structure Instance description language
|
||||
- Initial goal: Describing an instance of a data structure at one specific point in time.
|
||||
- Definitions:
|
||||
- Logical vs Physical state (set of records vs the way that those records are laid out on disk)
|
||||
- Approach: Commonalities between different data structures... standard patterns
|
||||
- Records
|
||||
- Pointers (to a address of a physical entity that describes a collection of records)
|
||||
|
|
@ -153,19 +408,83 @@
|
|||
</section>
|
||||
|
||||
<section>
|
||||
<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>
|
||||
<!-- Accessing Static Data Structures
|
||||
- Queries as morphisms on the language
|
||||
- Enumeration + Pop
|
||||
- Lookups
|
||||
- Scans
|
||||
- Enumeration via "Pop"
|
||||
- Implementing "Pop lowest"
|
||||
-->
|
||||
<!-- Dynamic Data
|
||||
- Definition: Physical vs logical state transitions: Dynamic data is a physiological transition.
|
||||
- Do the minimum work possible: Linked List
|
||||
-->
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<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>
|
||||
<!-- Optimizing Static Data Structures
|
||||
- Now we're talking about purely physical state transitions
|
||||
- Pattern + Replacement Language
|
||||
- Events
|
||||
- Examples
|
||||
|
|
@ -176,6 +495,18 @@
|
|||
</section>
|
||||
|
||||
<section>
|
||||
<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>
|
||||
<!-- Policy Discovery and Optimization
|
||||
- Purely Heuristic Design: Cracker Index / Transition Policy / Splay Trees
|
||||
- Assisted Discovery: Parameterized Search Space + Cost Model
|
||||
|
|
|
|||
Loading…
Reference in a new issue