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dijkstra.html
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<html>
<head>
<title>
DIJKSTRA - Demonstration of Dijkstra's Minimum Distance Algorithm
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
DIJKSTRA <br> Demonstration of Dijkstra's Minimum Distance Algorithm
</h1>
<hr>
<p>
<b>DIJKSTRA</b>
is a C++ library which
implements a simple version of Dijkstra's algorithm for determining
the minimum distance from one node in a graph to all other nodes.
</p>
<p>
The program is mainly of interest as a starting point for a parallelization
effort using OpenMP.
</p>
<p>
The example graph handled by the program has 6 nodes and 8 links,
each with a positive length:
<pre>
N0--15--N2-100--N3
\ | /
\ | /
40 20 10
\ | /
\ | /
N1
/ \
/ \
6 25
/ \
/ \
N5----8-----N4
</pre>
</p>
<p>
Using "Inf" to indicate that there is no link between two nodes,
the distance matrix for this graph is:
<pre>
0 40 15 Inf Inf Inf
40 0 20 10 25 6
15 20 0 100 Inf Inf
Inf 10 100 0 Inf Inf
Inf 25 Inf Inf 0 8
Inf 6 Inf Inf 8 0
</pre>
</p>
<p>
Dijkstra's algorithm efficiently determines the length of the shortest
path from node 0 to other nodes as:
<pre>
From 0 to: 0 1 2 3 4 5
Distance: 0 35 15 45 49 41
</pre>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>DIJKSTRA</b> is available in
<a href = "../../c_src/dijkstra/dijkstra.html">a C version</a> and
<a href = "../../cpp_src/dijkstra/dijkstra.html">a C++ version</a> and
<a href = "../../f77_src/dijkstra/dijkstra.html">a FORTRAN77 version</a> and
<a href = "../../f_src/dijkstra/dijkstra.html">a FORTRAN90 version</a> and
<a href = "../../m_src/dijkstra/dijkstra.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/bellman_ford/bellman_ford.html">
BELLMAN_FORD</a>,
a C++ library which
implements the Bellman-Ford algorithm for finding the shortest distance
from a given node to all other nodes in a directed graph whose
edges have been assigned real-valued lengths.
</p>
<p>
<a href = "../../cpp_src/dijkstra_openmp/dijkstra_openmp.html">
DIJKSTRA_OPENMP</a>,
a C++ program which
uses OpenMP to parallelize a simple example of Dijkstra's
minimum distance algorithm for graphs.
</p>
<p>
<a href = "../../cpp_src/floyd/floyd.html">
FLOYD</a>,
a C++ library which
implements Floyd's algorithm for finding the shortest distance between pairs of
nodes on a directed graph.
</p>
<p>
<a href = "../../cpp_src/toms097/toms097.html">
TOMS097</a>,
a C++ library which
computes the distance between all pairs of nodes in a directed graph
with weighted edges, using Floyd's algorithm.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Edsger Dijkstra,<br>
A note on two problems in connexion with graphs,<br>
Numerische Mathematik,<br>
Volume 1, 1959, pages 269-271.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "dijkstra.cpp">dijkstra.cpp</a>, the source code.
</li>
<li>
<a href = "dijkstra.sh">dijkstra.sh</a>,
commands to compile, link and run the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "dijkstra_output.txt">dijkstra_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> runs an example of Dijkstra's minimum distance algorithm.
</li>
<li>
<b>DIJKSTRA_DISTANCE</b> uses Dijkstra's minimum distance algorithm.
</li>
<li>
<b>FIND_NEAREST</b> finds the nearest unconnected node.
</li>
<li>
<b>INIT</b> initializes the problem data.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>UPDATE_MIND</b> updates the minimum distance vector.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 01 July 2010.
</i>
<!-- John Burkardt -->
</body>
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</html>