build based on b8728d6

This commit is contained in:
Documenter.jl
2023-08-21 10:01:57 +00:00
parent d9054bef63
commit afc5d2112a
19 changed files with 104 additions and 31 deletions

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@@ -31,7 +31,7 @@
"id": "ade31d26",
"metadata": {},
"source": [
"## The all pairs of shortest paths (ASP) problem\n",
"## The All Pairs of Shortest Paths (ASP) problem\n",
"\n",
"Let us start by presenting the all pairs of shortest paths (ASP) problem and its solution with the [FloydWarshall algorithm](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm).\n",
"\n",
@@ -70,10 +70,21 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 1,
"id": "4fe447c5",
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"floyd! (generic function with 1 method)"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function floyd!(C)\n",
" n = size(C,1)\n",
@@ -99,10 +110,25 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 2,
"id": "860e537c",
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"4×4 Matrix{Int64}:\n",
" 0 9 6 1\n",
" 2 0 8 3\n",
" 5 3 0 6\n",
" 10 8 5 0"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"inf = 1000\n",
"C = [\n",
@@ -296,7 +322,7 @@
"id": "db9a3294",
"metadata": {},
"source": [
"TODO explain this part"
"At each iteration, the processor needs the input values `C[i,j]`, `C[i,k]` and `C[k,j]`. Since we split the data row-wise, the process already has values `C[i,j]` and `C[i,k]`. However, `C[k,j]` may be stored in a different process. "
]
},
{
@@ -314,6 +340,14 @@
"</div>"
]
},
{
"cell_type": "markdown",
"id": "a01872ef",
"metadata": {},
"source": [
"As we iterate over columns $j$, the process needs input from all values of row $k$. Therefore, at the start of iteration $k$, the whole row $k$ needs to be communicated."
]
},
{
"attachments": {
"g12957.png": {
@@ -634,7 +668,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.9.0",
"display_name": "Julia 1.9.1",
"language": "julia",
"name": "julia-1.9"
},
@@ -642,7 +676,7 @@
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.9.0"
"version": "1.9.1"
}
},
"nbformat": 4,

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@@ -18,4 +18,4 @@
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