From df9f064facd3bf56794b13371b09c3d29d28c4c9 Mon Sep 17 00:00:00 2001 From: Oliver Date: Thu, 10 Oct 2019 19:05:35 -0400 Subject: [PATCH] Papers --- src/teaching/cse-662/2019fa/index.md | 13 +- .../cse-662/2019fa/slide/2019-10-08-STM.pptx | Bin 0 -> 708196 bytes .../2019fa/slide/2019-10-15-Legorithmics.erb | 463 ++++++++++++++++++ .../slide/graphics/Legorithmics-Paper3.png | Bin 0 -> 270175 bytes .../slide/graphics/Legorithmics-Paper4.png | Bin 0 -> 406453 bytes .../slide/graphics/Legorithmics-Paper5.png | Bin 0 -> 220558 bytes .../slide/graphics/Legorithmics-Paper6.png | Bin 0 -> 249494 bytes 7 files changed, 475 insertions(+), 1 deletion(-) create mode 100644 src/teaching/cse-662/2019fa/slide/2019-10-08-STM.pptx create mode 100644 src/teaching/cse-662/2019fa/slide/2019-10-15-Legorithmics.erb create mode 100644 src/teaching/cse-662/2019fa/slide/graphics/Legorithmics-Paper3.png create mode 100644 src/teaching/cse-662/2019fa/slide/graphics/Legorithmics-Paper4.png create mode 100644 src/teaching/cse-662/2019fa/slide/graphics/Legorithmics-Paper5.png create mode 100644 src/teaching/cse-662/2019fa/slide/graphics/Legorithmics-Paper6.png diff --git a/src/teaching/cse-662/2019fa/index.md b/src/teaching/cse-662/2019fa/index.md index d7c2477b..caff3ba6 100644 --- a/src/teaching/cse-662/2019fa/index.md +++ b/src/teaching/cse-662/2019fa/index.md @@ -36,7 +36,7 @@ about the group's report, deliverables, and any related tools and technology. their final project. A roughly 5-page report should outline the group’s proposed design, any algorithms or data structures being introduced, as well as a strategy for evaluating the resulting project against the current state - of the art. This report and presentation constitute 35% of the final grade. + of the art. This report and presentation constitute 15% of the final grade. 3. At the final stage, students are expected to provide a roughly 5-page report detailing their project, any algorithms or data structures developed, and evaluating their project against any comparable state of the art systems and @@ -53,6 +53,10 @@ about the group's report, deliverables, and any related tools and technology. * Oliver Kennedy (Capen 212; Office Hours TBD) * **Time**: TR 5:00-6:20 PM * **Location**: NSC 201 +* **Checkpoint Submissions** + * **Checkpoint 1**: Sept. 25 + * **Checkpoint 2**: Oct. 23 + * **Checkpoint 3**: Dec. 6 --- @@ -92,6 +96,13 @@ After the taking the course, students should be able to: * **Oct 1** - Interpretable Deep Learning ([reading 1](https://ieeexplore-ieee-org.gate.lib.buffalo.edu/abstract/document/8022871) | [reading 2](https://dl-acm-org.gate.lib.buffalo.edu/citation.cfm?Id=2939778)) * **Oct 3** - SkyServer on MonetDB presented by SQLatin ([reading](https://ieeexplore-ieee-org.gate.lib.buffalo.edu/abstract/document/4274958/) | slides) * **Oct 8** - Software Transactional Memory ([reading](https://dl.acm.org/citation.cfm?id=1378582)) +* **Oct 10** - Skyserver (continued) +* **Oct 15** - NoDB / RAW ([paper 1](http://dl-acm-org.gate.lib.buffalo.edu/citation.cfm?id=2213864) | [paper 2](http://www.vldb.org/pvldb/vol7/p1119-karpathiotakis.pdf)) +* **Oct 17** - Group Presentations +* **Oct 22** - Legorithmics ([paper](http://infoscience.epfl.ch/record/186017/files/main-final.pdf)) +* **Oct 24** - Streaming ([paper](http://www.cs.cornell.edu/johannes/papers/2007/2007-CIDR-Cayuga.pdf)) +* **Oct 29** - Scan Sharing ([paper](http://dl-acm-org.gate.lib.buffalo.edu/citation.cfm?id=1687707)) +* **Oct 31** - Group Presentations --- diff --git a/src/teaching/cse-662/2019fa/slide/2019-10-08-STM.pptx b/src/teaching/cse-662/2019fa/slide/2019-10-08-STM.pptx new file mode 100644 index 0000000000000000000000000000000000000000..568682146358cdb3d330a720f67983b8be255388 GIT binary patch literal 708196 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    +
    +

    Legorithmics

    +

    October 23, 2017

    +
    + +
    + + + + + + +

    Same great algorithms,
    awesome new hardware flavor

    +
    + + +
    +

    Adapting Software to Hardware

    + +

    Hardware adaptation uses standard transformations: +

      +
    • Batching: Prefetch blocks of data to avoid random seeks.
    • +
    • Partitioning: Group related blocks of data to minimize cross-partition work.
    • +
    • Reordering: Cluster data accesses for better cache locality.
    • +
    +

    +

    The hard part is picking where to apply the transformations and selecting values for the transformation's parameters

    +
    + +
    +

    Adapting Software to Hardware

    + +

    Key Insights: +

      +
    • The basic algorithms haven't changed since the 70s.
    • +
    • Hardware changes very slowly
    • +
    • You have as much time as you need to design a hardware-specific algorithm
    • +
    +

    +

    Automate the search!

    +
    + +
    +

    Adapting Software to Hardware

    + +

    What do we need?

    +
      +
    • A way to describe the algorithm.
    • +
    • A way to describe the hardware.
    • +
    • A cost model.
    • +
    • Transformation rules.
    • +
    • A (possibly exp-time) optimizer
    • +
    +
    + +
    + +
    +
    +

    Typesystems

    + +

    A collection of rules that assign a property called a type to the parts of a computer program: variables, expressions, etc...
    [Wikipedia]

    + +
    + +
    +

    Typesystems

    + +

    A typesystem allows you to: +

      +
    • Define interfaces between different parts of a program.
    • +
    • Check that these parts have been connected consistently.
    • +
    • Define global properties in terms of local properties.
    • +
    +

    + +
    + +
    +

    Typesystems

    + +
    +

    A type
    + ($\tau := D\;|\;[\tau]\;|<\tau,\tau>\;|\;\tau\rightarrow\tau$) +

    +
    +

    A set of inference rules
    + ($\frac{e\;:\;\tau}{[e]\;:\;[\tau]}$) +

    +
    +

    These example types are part of the monad algebra

    +
    + +
    +

    Types

    + + + + + + +
    TypeMeaning
    $D$Primitive Type (int, float, etc...)
    $[\tau]$An array of elements with type $\tau$
    $<\tau_1,\tau_2>$A pair of elements of types $\tau_1$ and $\tau_2$.
    $\tau_1\rightarrow\tau_2$A function with one argument of type $\tau_1$ and one return value of type $\tau_2$.
    +
    + +
    +

    Type Examples

    + +
    $[ < int,float > ]$
    +
    $[int] \rightarrow float$
    +
    $ < [int], [int] >\; \rightarrow [ < int,int > ]$
    +
    + +
    +

    Inference Rules

    +
    +

    Defined over a language of expressions like $f(a, b)$.

    + $$\frac{a : \tau_a\;\;\;b : \tau_b}{f(a,b):\tau_f(\tau_a, \tau_b)}$$ +

    If expression $a$ has type $\tau_a$ and expression $b$ has type $\tau_b$...

    +

    ...then expression $f(a, b)$ has type $\tau_f(\tau_a, \tau_b)$.

    +
    + +
    +

    Inference Examples

    +
    + $\frac{e: \tau}{[e] : [\tau]}$ +
    +
    + $\frac{c: Bool\;\;\;e_1:\tau\;\;\;e_2:\tau}{(\textbf{if}\;c\;\textbf{then}\;e_1\;\textbf{else}\;e_2)\;:\; \tau}$ +
    +
    + $\frac{e: < \tau_1, \tau_2 >\;\;\;i \in \{1,2\}}{e.i\; :\; \tau_i}$ +
    +
    +
    + +
    +
    +

    Monad Algebra

    + +

    A primitive language for describing data processing.

    + + + + + + +
    OperatorMeaning
    $\lambda x.e$Define a function with body $e$ that uses variable $x$.
    $e_1\;e_2$Apply the function defined by $e_1$ to the value obtained from $e_2$.
    $ \textbf{if}\;c\;\textbf{then}\;e_1\;\textbf{else}\;e_2$If $c$ is true then evaluate $e_1$, and otherwise evaluate $e_2$.
    + +
    +
    +

    Monad Algebra

    + + + + + + + + +
    OperatorMeaning
    $ < e_1, e_2 >$Construct a tuple from $e_1$ and $e_2$.
    $ e.i $Extract attribute $i$ from the tuple $e$.
    $ [e] $Construct a single-element array from e.
    $ [] $Construct an empty array.
    $ e_1 \sqcup e_2 $Concatenate the arrays $e_1$ and $e_2$.
    + +
    + +
    + $$\textbf{flatMap}(f : \tau_1 \rightarrow [\tau_2])(e : [\tau_1])$$ +

    Apply function $f$ to every element of array $e$. Concatenate all of the arrays returned by $f$.

    + + + $$\textbf{foldL}(c : \tau_2, f : < \tau_2, \tau_1 >)(e : [\tau_1])$$ +

    Apply function $f$ to every element of array $e$, with each invocation passing its return value to the next call (e.g., aggregation)

    + + $$\textbf{for}(xB : [\tau_1] [k] \leftarrow e_{in} : [\tau_1])(e_{loop} : [\tau_2])$$ +

    Extract blocks of size $k$ from $e_{in}$. For each block compute a flatMap using expression $e_{loop}$.

    + +

    + +
    +

    Example - Average

    + +
    + $(\lambda tot.(tot.1 / tot.2))$
    +      + $(\textbf{foldL}($ + $< 0, 0 >,$ + $(\lambda < a, x >.<$ + $a.1 + x$ + $,$ + $a.2 + 1$ + $ > $ + $))$ +
    +

    Fold implements aggregation

    +

    Fold takes a 'previous' $a$ and a 'current' $x$

    +

    We need a sum, and a count

    +

    Initial sum and count are both 0

    +

    Postprocess with division ($\lambda$ creates a variable $tot$)

    + +
    +
    + +
    +
    +

    Cost Estimation

    +

    We need... +

      +
    • Cardinality estimation
    • +
    • A model of IO
    • +
    • IO Cost relative to cardinality
    • +

    +
    + +
    +

    Cardinality Estimation

    + +

    Basic Approach: Define a second type for tracking data sizes

    + + $$\alpha\;:=\;[\alpha]^x\;|\;< \alpha_1, \alpha_2 >|\;c$$ + +
    +
    +

    e.g., $[ < 1, [1]^y > ]^x$ corresponds to: +

      +
    • an array with $x$ elements, where each element consists of...
    • +
    • a value of fixed-size 1, and...
    • +
    • an array of $y$ fixed-size values.
    • +

    +
    +
    + +
    +

    Cardinality Estimation

    + +
      +
    • $size(c) = c$
    • +
    • $size([\alpha]^x) = x \cdot size(\alpha)$
    • +
    • $size( < \alpha_1, \alpha_2 >) = size(\alpha_1) + size(\alpha_2)$
    • +
    +
    + +
    +

    Cardinality Estimation

    + +

    $R(\Gamma, e)$ computes the cardinality type for $e$

    +

    $\Gamma : x \rightarrow \alpha$ is a context / scope

    +
    + +
    +

    For Loops

    +
    + $$R\left(\Gamma, \textbf{for}(x [k] \leftarrow e_1)\; e_2\right) := $$ +

    + $\frac{cardinality(R(\Gamma, e_1))}{k}\cdot$ + $R(\Gamma', e_2)$ +

    +
    +
    $\Gamma' := \Gamma \cup \{x \mapsto [sizeofElement(R(\Gamma, e_1))]^k\}$
    +
    +

    The cardinality is based on that of $e_2$

    +

    Repeated once for every time through the loop

    +

    And $e_2$ is evaluated in the context of a $k$ element array.

    +
    + +
    +

    If Then Else

    +
    + $$R\left(\Gamma, \textbf{if}\;c\;\textbf{then}\;e_1\;\textbf{else}\;e_2\right) := $$ +

    + $max(R\left(\Gamma, e_1\right), R\left(\Gamma, e_2\right))$ +

    +

    Pessimistic assumption of biggest possible size.
    Avoids needing to estimate $p(c = true)$.

    +
    +
    + +
    +
    +

    Example: Block-Nested-Loop Join

    +
    +
    # Loop over blocks in outer rel.
    +
    $\textbf{for}( xB [k_1] \leftarrow R )$
    +
    # Loop over blocks in inner rel.
    +
    $\textbf{for}( yB [k_2] \leftarrow S )$
    +
    # Loop over elems in outer block.
    +
    $\textbf{for}( x \leftarrow xB )$
    +
    # Loop over elems in inner block.
    +
    $\textbf{for}( y \leftarrow yB )$
    +
    # Join test.
    +
    $\textbf{if}\;joinCond(x, y)$
    +
    # Add pair if success.
    +
    $\textbf{then}\;[< x, y >]$
    +
    # Add nothing if not.
    +
    $\textbf{else}\;[]$
    +
    +
    + +
    + + + + + + + + + + + + + + + + + + + + + + + +
    ExpressionContextResult Size
    $\textbf{for}( xB [k_1] \leftarrow R )$$\Gamma_1 = R \mapsto [1]^x, S \mapsto [1]^y$$[ < 1, 1 > ]^{\frac{x}{k_1} \cdot \frac{y}{k_2} \cdot k_1 \cdot k_2}$
    $\textbf{for}( yB [k_2] \leftarrow S )$$\Gamma_2 = \Gamma_1 \cup xB \mapsto [1]^{k_1}$$[ < 1, 1 > ]^{\frac{y}{k_2} \cdot k_1 \cdot k_2}$
    $\textbf{for}( x \leftarrow xB )$$\Gamma_3 = \Gamma_2 \cup yB \mapsto [1]^{k_2}$$[ < 1, 1 > ]^{k_1 \cdot k_2}$
    $\textbf{for}( y \leftarrow yB )$$\Gamma_4 = \Gamma_3 \cup x \mapsto 1$$[ < 1, 1 > ]^{k_2}$
    $\textbf{if}\;joinCond(x, y)$$\Gamma_5 = \Gamma_4 \cup y \mapsto 1$$[ < 1, 1 > ]^1$
    $\textbf{then}\;[< x, y >]$$\Gamma_5$$[ < 1, 1 > ]^1$
    $\textbf{else}\;[]$$\Gamma_5$$0$
    +
    +
    + +
    +
    +

    IO Model

    +

    IO Costs have 2 components: +

      +
    • $InitCom$: The cost of initializing a connection (e.g., seek time).
    • +
    • $UnitTr$: The cost of transferring one unit of data.
    • +

    +

    Costs are defined for every pair of memory hierarchy levels: +

      +
    • $UnitTr(HDD \rightarrow RAM)$ is the cost of reading from HDD into Ram.
    • +
    • $InitCom(RAM \rightarrow HDD)$ is the cost of seeking to a write from Ram onto a HDD.
    • +

    + +
    + +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    ExpressionResult SizeHDD to RAMRAM to HDD
    $\textbf{for}( xB [k_1] \leftarrow R )$$[ < 1, 1 > ]^{\frac{x}{k_1} \cdot \frac{y}{k_2} \cdot k_1 \cdot k_2}$$x+\frac{x}{k_1}y$$2xy$
    $\textbf{for}( yB [k_2] \leftarrow S )$$[ < 1, 1 > ]^{\frac{y}{k_2} \cdot k_1 \cdot k_2}$$y$$2k_1y$
    $\textbf{for}( x \leftarrow xB )$$[ < 1, 1 > ]^{k_1 \cdot k_2}$$0$$2k_1k_2$
    $\textbf{for}( y \leftarrow yB )$$[ < 1, 1 > ]^{k_2}$$0$$(1+1)k_2$
    $\textbf{if}\;joinCond(x, y)$$[ < 1, 1 > ]^1$$0$$(1+1)k_2$
    $\textbf{then}\;[< x, y >]$$[ < 1, 1 > ]^1$$0$$(1+1)k_2$
    $\textbf{else}\;[]$$0$$0$$0$
    +

    HDD: $R, S, Result$ RAM: $x, xB, y, yB$

    +
    +
    + +
    +
    +

    Rewrite Rules

    +

    Batching

    + $$for(x [1] \leftarrow R)\; e \Rightarrow for(xB [k] \leftarrow R)\; for(x [1] \leftarrow xB)\; e$$ + +

    Reordering Iterators

    + $$for(x_1 [k_1] \leftarrow R_1)\;for(x_2 [k_2] \leftarrow R_2) \Rightarrow$$ + $$for(x_2 [k_2] \leftarrow R_2)\;for(x_1 [k_1] \leftarrow R_1)$$ + +

    Size-Dependent, Commutative Functions

    + $$f \Rightarrow (\lambda< x_1, x_2>.f(\textbf{if}\;|x_1|\leq |x_2|\;\textbf{then}< x_1, x_2 >\;\textbf{else}\;< x_2, x_1 >))$$ + $$f \Rightarrow (\lambda< x_1, x_2>.f(\textbf{if}\;|x_1|\leq |x_2|\;\textbf{then}< x_2, x_1 >\;\textbf{else}\;< x_1, x_2 >))$$ +
    + +
    +

    The Optimizer

    + Starting with $e$... +
      +
    1. For every possible rewrite of $e$:
    2. +
    3. Use a linear optimizer to find the best $k$s
    4. +
    5. If the rewrite improved the cost then recur.
    6. +
    +
    + +
    +

    Legorithmics

    +
      +
    • Define your algorithms once.
    • +
    • Define your hardware spec once.
    • +
    • Let an automatic tool fit the algoroithm to the hardware!
    • +
    +
    +
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