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<html>
<head>
<title>
DIJKSTRA_SPMD - Parallel Version of Dijkstra's Minimum Distance Algorithm
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
DIJKSTRA_SPMD <br> Parallel Version of Dijkstra's Minimum Distance Algorithm
</h1>
<hr>
<p>
<b>DIJKSTRA_SPMD</b>
is a MATLAB program which
runs a simple demonstration of Dijkstra's algorithm for determining
the minimum distance from one node in a graph to all other nodes,
using the SPMD command to carry out the task in parallel.
</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_SPMD</b> is available in
<a href = "../../m_src/dijkstra_spmd/dijkstra_spmd.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/contrast_spmd/contrast_spmd.html">
CONTRAST_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature for image operations;
the client reads an image, the workers increase contrast over separate portions, and
the client assembles and displays the results.
</p>
<p>
<a href = "../../m_src/contrast2_spmd/contrast2_spmd.html">
CONTRAST2_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature for image operations;
this improves the contrast_spmd program by allowing the workers to share some
data; this makes it possible to eliminate artificial "seams" in the processed
image.
</p>
<p>
<a href = "../../m_src/dijkstra/dijkstra.html">
DIJKSTRA</a>,
a MATLAB program which
runs a simple example of Dijkstra's minimum distance algorithm for graphs.
</p>
<p>
<a href = "../../c_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 = "../../m_src/face_spmd/face_spmd.html">
FACE_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature;
the client has a 3D box that has been dissected into tetrahedrons.
Multiple workers cooperate to construct a list of the triangular faces
that lie on the boundaries of the box.
</p>
<p>
<a href = "../../m_src/fd2d_heat_explicit_spmd/fd2d_heat_explicit_spmd.html">
FD2D_HEAT_EXPLICIT_SPMD</a>,
a MATLAB program which
uses the finite difference method and explicit time stepping
to solve the time dependent heat equation in 2D. A black and white image
is used as the "initial condition". MATLAB's SPMD facility is used to
carry out the computation in parallel.
</p>
<p>
<a href = "../../m_src/image_denoise_spmd/image_denoise_spmd.html">
IMAGE_DENOISE_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature for image operations;
the client reads an image, the workers process portions of it, and
the client assembles and displays the results.
</p>
<p>
<a href = "../../m_src/matrix_assemble_spmd/matrix_assemble_spmd.html">
MATRIX_ASSEMBLE_SPMD</a>,
a MATLAB program which
demonstrates the SPMD parallel programming feature by having each worker
assemble part of the Hilbert matrix, which is then combined into one
array by the client program.
</p>
<p>
<a href = "../../m_src/prime_spmd/prime_spmd.html">
PRIME_SPMD</a>,
a MATLAB program which
counts the number of primes between 1 and N;
running in parallel using MATLAB's "SPMD" feature.
</p>
<p>
<a href = "../../m_src/quad_spmd/quad_spmd.html">
QUAD_SPMD</a>,
a MATLAB program which
estimates an integral using quadrature;
running in parallel using MATLAB's "SPMD" feature.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
The User's Guide for the Parallel Computing Toolbox is available at
<a href = "http://www.mathworks.com/access/helpdesk/help/pdf_doc/distcomp/distcomp.pdf">
http://www.mathworks.com/access/helpdesk/help/pdf_doc/distcomp/distcomp.pdf</a>
</p>
<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>
<li>
Gaurav Sharma, Jos Martin,<br>
MATLAB: A Language for Parallel Computing,<br>
International Journal of Parallel Programming,<br>
Volume 37, Number 1, pages 3-36, February 2009.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "dijkstra_fun.m">dijkstra_fun.m</a>,
carries out Dijkstra's minimum distance algorithm.
</li>
<li>
<a href = "dijkstra_fsu.m">dijkstra_fsu.m</a>,
runs an example of Dijkstra's minimum distance algorithm
on the FSU HPC cluster.
</li>
<li>
<a href = "dijkstra_spmd.m">dijkstra_spmd.m</a>,
runs an example of Dijkstra's minimum distance algorithm.
(Issue a MATLABPOOL command first to set up workers)
</li>
<li>
<a href = "initial_distance.m">initial_distance.m</a>,
initializes the distance matrix.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a timestamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "dijkstra_spmd_output.txt">dijkstra_spmd_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 21 March 2011.
</i>
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