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@@ -124,6 +124,7 @@ makedocs(;
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"MPI" => "notebooks/mpi_tutorial.md",
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"Matrix Multiplication"=>"notebooks/matrix_matrix.md",
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"Jacobi" => "notebooks/jacobi_method.md",
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"ASP" => "notebooks/asp.md",
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"Solutions" => "notebooks/solutions.md"
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]],
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)
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+16
-92
@@ -22,7 +22,7 @@
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"\n",
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"In this notebook, we will learn\n",
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"\n",
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"- How to parallelize the Floyd's algorithm\n",
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"- How to parallelize Floyd's algorithm\n",
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"- How communication can affect the correctness of a distributed algorithm\n"
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]
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},
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@@ -33,14 +33,14 @@
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"source": [
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"## The all pairs of shortest paths (ASP) problem\n",
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"\n",
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"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",
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"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",
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"\n",
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"### Problem statement\n",
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"\n",
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"- Given a graph $G$ with a distance table $C$\n",
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"- Compute the length of the shortest path between any two nodes in $G$\n",
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"\n",
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"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"
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"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"
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]
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},
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{
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@@ -70,21 +70,10 @@
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"execution_count": null,
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"id": "4fe447c5",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"floyd! (generic function with 1 method)"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"function floyd!(C)\n",
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" n = size(C,1)\n",
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@@ -415,21 +404,10 @@
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": null,
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"id": "09937668",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"rand_distance_table (generic function with 1 method)"
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]
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},
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"execution_count": 1,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"function rand_distance_table(n)\n",
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" threshold = 0.4\n",
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@@ -451,31 +429,10 @@
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": null,
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"id": "3116096c",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"10×10 Matrix{Int64}:\n",
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" 0 3 100000 100000 100000 … 3 100000 7 100000\n",
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" 8 0 3 10 5 9 9 10 10\n",
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" 100000 7 0 100000 8 100000 100000 7 7\n",
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" 3 100000 6 0 7 9 5 10 10\n",
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" 10 5 100000 7 0 100000 100000 8 100000\n",
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" 5 10 100000 3 9 … 4 10 7 100000\n",
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" 100000 9 8 10 100000 0 4 100000 4\n",
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" 5 10 9 100000 6 100000 0 5 100000\n",
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" 3 10 7 10 3 4 100000 0 100000\n",
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" 10 100000 9 4 6 3 100000 7 0"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"rand_distance_table(10)"
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]
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@@ -500,21 +457,10 @@
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": null,
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"id": "6bc0122b",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"MPI.ThreadLevel(2)"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"using MPIClusterManagers\n",
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"using Distributed\n",
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@@ -536,21 +482,10 @@
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"execution_count": null,
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"id": "22234b2f",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"floyd_dist! (generic function with 1 method)"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"function floyd_dist!(C)\n",
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" m = size(C,1)\n",
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@@ -567,7 +502,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"execution_count": null,
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"id": "d5a8d3a8",
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"metadata": {},
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"outputs": [],
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@@ -603,21 +538,10 @@
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"execution_count": null,
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"id": "dd77ee3d",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"\u001b[32m\u001b[1mTest Passed\u001b[22m\u001b[39m"
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]
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},
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"execution_count": 24,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"using Test\n",
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"load = 10\n",
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+74
-2
@@ -1,5 +1,77 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "533363df",
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"metadata": {},
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"source": [
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"<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/3/39/VU_logo.png/800px-VU_logo.png?20161029201021\" width=\"350\">\n",
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"\n",
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"### Programming large-scale parallel systems\n",
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"\n",
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"# Traveling sales person"
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]
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},
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{
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"cell_type": "markdown",
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"id": "98ebaf0c",
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"metadata": {},
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"source": [
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"## Contents\n",
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"\n",
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"In this notebook, we will learn\n",
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"\n",
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"- How to parallelize the solution of the traveling sales person problem\n",
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"- The concept of search overhead\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "14864a1b",
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"metadata": {},
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"source": [
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"## The traveling sales person (TSP) problem\n",
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"\n",
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"Let us start by presenting the [traveling sales person (ASP) problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem) and its solution using a [branch and bound algorithm](https://en.wikipedia.org/wiki/Branch_and_bound).\n",
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"\n",
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"### Problem statement\n",
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"\n",
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"- Given a graph $G$ with a distance table $C$ and an initial node (i.e. a city) in the graph\n",
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"- Compute the shortest route that visits all cities exactly once, without returning to the initial city.\n",
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"\n",
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"\n",
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"Note that there we consider a version of the problem in which do not return to the initial city. However, the classic version of the problem includes returning to the initial city.\n",
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"\n",
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"\n",
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"As for the ASP problem 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 TSP problem for a simple 4-node graph. "
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]
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},
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{
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"attachments": {
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"g18228.png": {
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"image/png": 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truncated
|
||||
}
|
||||
},
|
||||
"cell_type": "markdown",
|
||||
"id": "14ae7875",
|
||||
"metadata": {},
|
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"source": [
|
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"<div>\n",
|
||||
"<img src=\"attachment:g18228.png\" align=\"left\" width=\"450\"/>\n",
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "aca8b2c4",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"### Branch and bound algorithm\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
@@ -256,7 +328,7 @@
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Julia 1.9.1",
|
||||
"display_name": "Julia 1.9.0",
|
||||
"language": "julia",
|
||||
"name": "julia-1.9"
|
||||
},
|
||||
@@ -264,7 +336,7 @@
|
||||
"file_extension": ".jl",
|
||||
"mimetype": "application/julia",
|
||||
"name": "julia",
|
||||
"version": "1.9.1"
|
||||
"version": "1.9.0"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
Reference in new issue
Block a user