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<html>
<head>
<title>
CITIES - City Distance Tools
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CITIES <br> City Distance Tools
</h1>
<hr>
<p>
<b>CITIES</b>
is a MATLAB library which
works with problems involving intercity distances.
</p>
<p>
Such problems include:
<ul>
<li>
traveling salesman problems (connected path through every city);
</li>
<li>
K-means calculations (find M spots that minimize total of the
distance from each city to its nearest spot);
</li>
<li>
K-medians calculations (make M of the cities "special", to minimize
the total distance from each city to its nearest special city);
</li>
<li>
Weighted K-means or K-medians (let the population of each city
be used as a weight, which makes some cities more important);
</li>
<li>
Minimal spanning trees (construct the shortest highway
system that connects all the cities, using only straight paths
from one city to another (ignore the possibility that two roads
could cross, or that a Y-shaped connector between three cities
might be cheaper);
</li>
<li>
Voronoi diagrams (assign each spot of land to the nearest city,
making "provinces");
</li>
</ul>
</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>CITIES</b> is available in
<a href = "../../cpp_src/cities/cities.html">a C++ version</a> and
<a href = "../../f_src/cities/cities.html">a FORTRAN90 version</a> and
<a href = "../../m_src/cities/cities.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/asa058/asa058.html">
ASA058</a>,
a MATLAB library which
contains the original text of the Sparks clustering algorithm.
</p>
<p>
<a href = "../../m_src/asa136/asa136.html">
ASA136</a>,
a MATLAB library which
implements the K-Means algorithm.
</p>
<p>
<a href = "../../datasets/cities/cities.html">
CITIES</a>,
a dataset directory which
contains a number of city distance datasets.
</p>
<p>
<a href = "../../m_src/distance_to_position/distance_to_position.html">
DISTANCE_TO_POSITION</a>,
a MATLAB program which
estimates the positions of cities based on a city-to-city distance table.
</p>
<p>
<a href = "../../m_src/distance_to_position_sphere/distance_to_position_sphere.html">
DISTANCE_TO_POSITION_SPHERE</a>,
a MATLAB program which
estimates the positions of cities on a sphere (such as the earth)
based on a city-to-city distance table.
</p>
<p>
<a href = "../../m_src/floyd/floyd.html">
FLOYD</a>,
a MATLAB library which
implements Floyd's algorithm for finding the shortest distance between pairs of
nodes on a directed graph.
</p>
<p>
<a href = "../../datasets/tsp/tsp.html">
TSP</a>,
a dataset directory which
contains test data for the traveling salesperson problem;
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Franz Aurenhammer,<br>
Voronoi diagrams -
a study of a fundamental geometric data structure,<br>
ACM Computing Surveys,<br>
Volume 23, Number 3, pages 345-405, September 1991.
</li>
<li>
John Burkardt, Max Gunzburger, Janet Peterson, Rebecca Brannon,<br>
User Manual and Supporting Information for Library of Codes
for Centroidal Voronoi Placement and Associated Zeroth,
First, and Second Moment Determination,<br>
Sandia National Laboratories Technical Report SAND2002-0099,<br>
February 2002.
</li>
<li>
Marc de Berg, Marc Krevald, Mark Overmars,
Otfried Schwarzkopf,<br>
Computational Geometry,<br>
Springer, 2000.
</li>
<li>
Qiang Du, Vance Faber, Max Gunzburger,<br>
Centroidal Voronoi Tessellations: Applications and Algorithms,<br>
SIAM Review, Volume 41, 1999, pages 637-676.
</li>
<li>
Alan Gibbons,<br>
Algorithmic Graph Theory,<br>
Cambridge University Press, 1985.
</li>
<li>
John Hartigan, M A Wong,<br>
Algorithm AS 136: A K-Means Clustering Algorithm,<br>
Applied Statistics,<br>
Volume 28, Number 1, 1979, pages 100-108.
</li>
<li>
Barry Joe, <br>
GEOMPACK - a software package for the generation of meshes
using geometric algorithms, <br>
Advances in Engineering Software,<br>
Volume 13, pages 325-331, 1991.
</li>
<li>
Hang Tong Lau,<br>
Algorithms on Graphs,<br>
Tab Books, 1989.
</li>
<li>
Atsuyuki Okabe, Barry Boots, Kokichi Sugihara, Sung Nok Chiu,<br>
Spatial Tesselations:
Concepts and Applications of Voronoi Diagrams,<br>
Second Edition,<br>
Wiley, 2000.
</li>
<li>
Joseph O'Rourke,<br>
Computational Geometry,<br>
Cambridge University Press,<br>
Second Edition, 1998.
</li>
<li>
Helmut Spaeth,<br>
Cluster Analysis Algorithms
for Data Reduction and Classification of Objects,<br>
Ellis Horwood, 1980.
</li>
<li>
David Sparks,<br>
Algorithm AS 58: Euclidean Cluster Analysis,<br>
Applied Statistics,<br>
Volume 22, Number 1, 1973,<br>
pages 126-130.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "dist_table_check.m">dist_table_check.m</a>,
checks a distance table.
</li>
<li>
<a href = "file_column_count.m">file_column_count.m</a>,
counts the number of columns in the first line of a file.
</li>
<li>
<a href = "file_exist.m">file_exist.m</a>,
reports whether a file exists.
</li>
<li>
<a href = "file_row_count.m">file_row_count.m</a>,
counts the number of row records in a file.
</li>
<li>
<a href = "i4_sign.m">i4_sign.m</a>,
returns the sign of an I4.
</li>
<li>
<a href = "i4_to_a.m">i4_to_a.m</a>,
returns the I-th alphabetic character;
</li>
<li>
<a href = "ll_rad_sphere_dist.m">ll_rad_sphere_dist.m</a>,
computes the great circle distance between two points on a sphere
of given radius, where the positions are given as latitude and longitude
in radians.
</li>
<li>
<a href = "point_to_dist_table.m">point_to_dist_table.m</a>,
returns a distance table given a set of point coordinates.
</li>
<li>
<a href = "r8mat_data_read.m">r8mat_data_read.m</a>,
reads a table from an R8MAT file.
</li>
<li>
<a href = "r8mat_header_read.m">r8mat_header_read.m</a>,
reads a table header from an R8MAT file.
</li>
<li>
<a href = "r8mat_print.m">r8mat_print.m</a>,
prints an R8MAT.
</li>
<li>
<a href = "r8mat_print_some.m">r8mat_print_some.m</a>,
prints some of an R8MAT.
</li>
<li>
<a href = "r8mat_transpose_print.m">r8mat_transpose_print.m</a>,
prints the transpose of an R8MAT.
</li>
<li>
<a href = "r8mat_transpose_print_some.m">
r8mat_transpose_print_some.m</a>,
prints the transpose of some of an R8MAT.
</li>
<li>
<a href = "r8mat_write.m">r8mat_write.m</a>,
writes an R8MAT file.
</li>
<li>
<a href = "r8vec_print.m">r8vec_print.m</a>,
prints an R8VEC;
</li>
<li>
<a href = "s_word_count.m">s_word_count.m</a>,
counts the number of words in a string.
</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 = "cities_test.m">cities_test.m</a>,
calls all the tests.
</li>
<li>
<a href = "cities_test01.m">cities_test01.m</a>,
tests XY_TO_DIST.
</li>
<li>
<a href = "spaeth2_09.txt">spaeth2_09.txt</a>,
a distance table.
</li>
<li>
<a href = "cities_test_output.txt">cities_test_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 19 September 2009.
</i>
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