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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 FORTRAN90 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 = "../../f_src/asa058/asa058.html">
ASA058</a>,
a FORTRAN90 library which
contains the original text of the Sparks
clustering algorithm.
</p>
<p>
<a href = "../../f_src/asa136/asa136.html">
ASA136</a>,
a FORTRAN90 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 = "../../f_src/distance_to_position/distance_to_position.html">
DISTANCE_TO_POSITION</a>,
a FORTRAN90 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 = "../../f_src/floyd/floyd.html">
FLOYD</a>,
a FORTRAN90 library which
implements Floyd's algorithm for finding the shortest distance between pairs of
nodes on a directed graph.
</p>
<p>
<a href = "../../data/graph_representation/graph_representation.html">
GRAPH_REPRESENTATION</a>,
a data directory which
contains examples of ways of representing abstract
mathematical graphs
</p>
<p>
<a href = "../../f_src/kmeans/kmeans.html">
KMEANS</a>,
a FORTRAN90 library which
treats the K-means
problem of grouping a discrete set of N points into K clusters.
</p>
<p>
<a href = "../../f_src/lau_np/lau_np.html">
LAU_NP</a>,
a FORTRAN90 library which
includes heuristic approaches
to certain NP-complete problems, including the traveling salesman
problem, the K-center problem and the K-median problem.
</p>
<p>
<a href = "../../f_src/point_merge/point_merge.html">
POINT_MERGE</a>,
a FORTRAN90 library which
considers N points in M dimensional space, and counts or indexes
the unique or "tolerably unique" items.
</p>
<p>
<a href = "../../f_src/spaeth/spaeth.html">
SPAETH</a>,
a FORTRAN90 library which
can cluster data according to various principles.
</p>
<p>
<a href = "../../datasets/spaeth/spaeth.html">
SPAETH</a>,
a dataset collection which
contains a set of test data.
</p>
<p>
<a href = "../../f_src/spaeth2/spaeth2.html">
SPAETH2</a>,
a FORTRAN90 library which
can cluster data according to various principles.
</p>
<p>
<a href = "../../datasets/spaeth2/spaeth2.html">
SPAETH2</a>,
a dataset collection which
contains a set of test data.
</p>
<p>
<a href = "../../f77_src/toms456/toms456.html">
TOMS456</a>,
a FORTRAN77 library which
solves the routing problem, connecting some nodes
in a network.
</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 = "cities.f90">cities.f90</a>, the source code.
</li>
<li>
<a href = "cities.sh">cities.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "cities_prb.f90">cities_prb.f90</a>,
a sample problem.
</li>
<li>
<a href = "cities_prb.sh">cities_prb.sh</a>,
commands to compile and run the problem.
</li>
<li>
<a href = "spaeth2_09_dist.txt">spaeth2_09_dist.txt</a>,
a distance table.
</li>
<li>
<a href = "wg22_dist.txt">wg22_dist.txt</a>,
a distance table.
</li>
<li>
<a href = "uscap_xy.txt">uscap_xy.txt</a>,
the coordinates of the US state capitols, using a cylindrical projection.
</li>
<li>
<a href = "cities_prb_output.txt">cities_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is a case insensitive comparison of two characters for equality.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the value of a base 10 digit.
</li>
<li>
<b>DEGREES_TO_RADIANS</b> converts an angle from degrees to radians.
</li>
<li>
<b>DIST_TABLE_CHECK</b> checks a distance table.
</li>
<li>
<b>DMS_PRINT</b> prints the latitude and longitude in degrees/minutes/seconds.
</li>
<li>
<b>DMS_READ</b> reads DMS data from a file.
</li>
<li>
<b>DMS_TO_DIST</b> creates a distance table from latitudes and longitudes.
</li>
<li>
<b>DMS_TO_DISTANCE_EARTH</b> finds the distance between two points on the earth.
</li>
<li>
<b>DMS_TO_RADIANS</b> converts degrees, minutes, seconds to radians.
</li>
<li>
<b>DMS_TO_XY:</b> Latitude/Longitude in DMS to XY coordinates.
</li>
<li>
<b>DMS_WRITE</b> writes a DMS latitude, longitude file.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_EXIST</b> reports whether a file exists.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4_SIGN</b> evaluates the sign of an I4.
</li>
<li>
<b>I4_TO_A</b> returns the I-th alphabetic character.
</li>
<li>
<b>LAT_CHAR</b> returns a character for negative or positive latitude.
</li>
<li>
<b>LL_DEGREES_TO_DIST</b> creates a distance table from latitudes and longitudes.
</li>
<li>
<b>LL_DEGREES_TO_DISTANCE_EARTH:</b> distance between two points on the earth.
</li>
<li>
<b>LL_DEGREES_TO_XY:</b> Latitude/Longitude in degrees to XY coordinates.
</li>
<li>
<b>LL_RAD_DIST_SPHERE:</b> spherical distance, latitude and longitude in radians.
</li>
<li>
<b>LONG_CHAR</b> returns a character for negative or positive longitude.
</li>
<li>
<b>MAIN_READ_CODE</b> reads the name of the code file from the main file.
</li>
<li>
<b>MAIN_READ_DIST</b> reads the name of the distance file from the main file.
</li>
<li>
<b>MAIN_READ_DMS</b> reads the name of the DMS file from the main file.
</li>
<li>
<b>MAIN_READ_GEOM</b> reads the name of the geometry from the main file.
</li>
<li>
<b>MAIN_READ_NAME</b> reads the name of the name file from the main file.
</li>
<li>
<b>MAIN_READ_SIZE</b> reads the problem size N from the main file.
</li>
<li>
<b>MAIN_READ_XY</b> reads the name of the XY file from the main file.
</li>
<li>
<b>POINT_TO_DIST_TABLE</b> creates a distance table from Cartesian coordinates.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads data from an R8MAT file.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>R8VEC_PRINT</b> prints a real vector.
</li>
<li>
<b>R8VEC2_DATA_READ</b> reads data from an R8VEC2 file.
</li>
<li>
<b>R8VEC2_HEADER_READ</b> reads the header from an R8VEC2 file.
</li>
<li>
<b>R8VEC2_PRINT</b> prints an R8VEC2.
</li>
<li>
<b>R8VEC2_WRITE</b> writes an R8VEC2 file.
</li>
<li>
<b>S_CAT</b> concatenates two strings to make a third string.
</li>
<li>
<b>S_EQI</b> is a case insensitive comparison of two strings for equality.
</li>
<li>
<b>S_REP_ONE</b> replaces the first occurrence of SUB1 with SUB2.
</li>
<li>
<b>S_TO_I4</b> reads an I4 from a string.
</li>
<li>
<b>S_TO_R8</b> reads an R8 from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads an R8VEC from a string.
</li>
<li>
<b>S_TO_W</b> reads the next blank-delimited word from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>WORD_NEXT_READ</b> "reads" words from a string, one at a time.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 15 July 2011.
</i>
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