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108
dev/notebooks/asp.ipynb
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@@ -22,7 +22,7 @@
"\n",
"In this notebook, we will learn\n",
"\n",
"- How to parallelize the Floyd's algorithm\n",
"- How to parallelize Floyd's algorithm\n",
"- How communication can affect the correctness of a distributed algorithm\n"
]
},
@@ -33,14 +33,14 @@
"source": [
"## The all pairs of shortest paths (ASP) problem\n",
"\n",
"Let us start by presenting the all pairs of shortest path (ASP) problem and its solution with the [Floyd–Warshall algorithm](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm).\n",
"Let us start by presenting the all pairs of shortest paths (ASP) problem and its solution with the [Floyd–Warshall algorithm](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm).\n",
"\n",
"### Problem statement\n",
"\n",
"- Given a graph $G$ with a distance table $C$\n",
"- Compute the length of the shortest path between any two nodes in $G$\n",
"\n",
"We represent the distance table as a matrix, where $C_{ij}$ is the distance from node $i$ to node $j$. Next figure shows the input and solution (output) of the ASP problem for a simple 4-node directed graph. For example, the solution of the problem contains the minimum distance from node 2 to node 3, which is $C_{23}=8$ as highlighted in the figure.\n"
"We represent the distance table as a matrix, where $C_{ij}$ is the distance from node $i$ to node $j$. Next figure shows the input and solution (output) of the ASP problem for a simple 4-node directed graph. Note that the minimum distance from node 2 to node 3, which is $C_{23}=8$ as highlighted in the figure.\n"
]
},
{
@@ -70,21 +70,10 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": null,
"id": "4fe447c5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"floyd! (generic function with 1 method)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"outputs": [],
"source": [
"function floyd!(C)\n",
" n = size(C,1)\n",
@@ -415,21 +404,10 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": null,
"id": "09937668",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"rand_distance_table (generic function with 1 method)"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"outputs": [],
"source": [
"function rand_distance_table(n)\n",
" threshold = 0.4\n",
@@ -451,31 +429,10 @@
},
{
"cell_type": "code",
"execution_count": 3,
"execution_count": null,
"id": "3116096c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"10×10 Matrix{Int64}:\n",
" 0 3 100000 100000 100000 … 3 100000 7 100000\n",
" 8 0 3 10 5 9 9 10 10\n",
" 100000 7 0 100000 8 100000 100000 7 7\n",
" 3 100000 6 0 7 9 5 10 10\n",
" 10 5 100000 7 0 100000 100000 8 100000\n",
" 5 10 100000 3 9 … 4 10 7 100000\n",
" 100000 9 8 10 100000 0 4 100000 4\n",
" 5 10 9 100000 6 100000 0 5 100000\n",
" 3 10 7 10 3 4 100000 0 100000\n",
" 10 100000 9 4 6 3 100000 7 0"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"outputs": [],
"source": [
"rand_distance_table(10)"
]
@@ -500,21 +457,10 @@
},
{
"cell_type": "code",
"execution_count": 2,
"execution_count": null,
"id": "6bc0122b",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"MPI.ThreadLevel(2)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"outputs": [],
"source": [
"using MPIClusterManagers\n",
"using Distributed\n",
@@ -536,21 +482,10 @@
},
{
"cell_type": "code",
"execution_count": 3,
"execution_count": null,
"id": "22234b2f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"floyd_dist! (generic function with 1 method)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"outputs": [],
"source": [
"function floyd_dist!(C)\n",
" m = size(C,1)\n",
@@ -567,7 +502,7 @@
},
{
"cell_type": "code",
"execution_count": 23,
"execution_count": null,
"id": "d5a8d3a8",
"metadata": {},
"outputs": [],
@@ -603,21 +538,10 @@
},
{
"cell_type": "code",
"execution_count": 24,
"execution_count": null,
"id": "dd77ee3d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"outputs": [],
"source": [
"using Test\n",
"load = 10\n",

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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>- · XM_40017</title><script data-outdated-warner src="../../assets/warner.js"></script><link rel="canonical" href="https://fverdugo.github.io/XM_40017/notebooks/asp/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script><link href="../../assets/favicon.ico" rel="icon" type="image/x-icon"/><script src="../../assets/iframeResizer.min.js"></script><link href="../../assets/custom.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="XM_40017 logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../">XM_40017</a></span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../getting_started_with_julia/">Getting started</a></li><li><span class="tocitem">Notebooks</span><ul><li><a class="tocitem" href="../julia_basics/">Julia Basics</a></li><li><a class="tocitem" href="../julia_async/">Tasks and channels</a></li><li><a class="tocitem" href="../julia_distributed/">Remote calls and remote channels</a></li><li><a class="tocitem" href="../mpi_tutorial/">MPI</a></li><li><a class="tocitem" href="../matrix_matrix/">Matrix Multiplication</a></li><li><a class="tocitem" href="../jacobi_method/">Jacobi</a></li><li><a class="tocitem" href="../solutions/">Solutions</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>-</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>-</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/fverdugo/XM_40017/blob/main/docs/src/notebooks/asp.ipynb" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><div class="admonition is-success">
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>ASP · XM_40017</title><script data-outdated-warner src="../../assets/warner.js"></script><link rel="canonical" href="https://fverdugo.github.io/XM_40017/notebooks/asp/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script><link href="../../assets/favicon.ico" rel="icon" type="image/x-icon"/><script src="../../assets/iframeResizer.min.js"></script><link href="../../assets/custom.css" rel="stylesheet" type="text/css"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="XM_40017 logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../">XM_40017</a></span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../getting_started_with_julia/">Getting started</a></li><li><span class="tocitem">Notebooks</span><ul><li><a class="tocitem" href="../julia_basics/">Julia Basics</a></li><li><a class="tocitem" href="../julia_async/">Tasks and channels</a></li><li><a class="tocitem" href="../julia_distributed/">Remote calls and remote channels</a></li><li><a class="tocitem" href="../mpi_tutorial/">MPI</a></li><li><a class="tocitem" href="../matrix_matrix/">Matrix Multiplication</a></li><li><a class="tocitem" href="../jacobi_method/">Jacobi</a></li><li class="is-active"><a class="tocitem" href>ASP</a></li><li><a class="tocitem" href="../solutions/">Solutions</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Notebooks</a></li><li class="is-active"><a href>ASP</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>ASP</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/fverdugo/XM_40017/blob/main/docs/src/notebooks/asp.ipynb" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><div class="admonition is-success">
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@@ -18,4 +18,4 @@
var myIframe = document.getElementById("notebook");
iFrameResize({log:true}, myIframe);
});
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