CITIES
City Distance Tools

CITIES is a library of FORTRAN90 routines, using double precision arithmetic, for working with problems involving intercity distances.

Such problems include:

• traveling salesman problems (connected path through every city);
• K-means calculations (find M spots that minimize total of the distance from each city to its nearest spot);
• K-medians calculations (make M of the cities "special", to minimize the total distance from each city to its nearest special city);
• Weighted K-means or K-medians (let the population of each city be used as a weight, which makes some cities more important);
• 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);
• Voronoi diagrams (assign each spot of land to the nearest city, making "provinces");

Related Data and Programs:

ASA058 is a FORTRAN77 library which contains the original text of the Sparks clustering algorithm.

ASA136 is a FORTRAN77 implementation of the K-Means algorithm.

CITIES is a dataset directory which contains a number of city distance datasets.

KMEANS is a FORTRAN90 library which treats the K-means problem of grouping a discrete set of N points into K clusters.

LAU_NP is 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.

PLOT_POINTS is a FORTRAN90 program which can plot the cities.

SPAETH is a FORTRAN90 library which can cluster data according to various principles.

SPAETH is a dataset collection which contains a set of test data.

SPAETH2 is a library of FORTRAN90 routines which can cluster data according to various principles.

SPAETH2 is a dataset collection which contains a set of test data.

TOMS456 is a routine for the routing problem, connecting some nodes in a network.

Reference:

1. Franz Aurenhammer,
   Voronoi diagrams - a study of a fundamental geometric data structure,
   ACM Computing Surveys,
   Volume 23, Number 3, pages 345-405, September 1991,
   ../../pdf/aurenhammer.pdf
2. John Burkardt, Max Gunzburger, Janet Peterson, Rebecca Brannon,
   User Manual and Supporting Information for Library of Codes for Centroidal Voronoi Placement and Associated Zeroth, First, and Second Moment Determination,
   Sandia National Laboratories Technical Report SAND2002-0099,
   February 2002,
   ../../publications/bgpb_2002.pdf
3. Marc de Berg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
   Computational Geometry,
   Springer, 2000.
4. Qiang Du, Vance Faber, Max Gunzburger,
   Centroidal Voronoi Tessellations: Applications and Algorithms,
   SIAM Review, Volume 41, 1999, pages 637-676.
5. Alan Gibbons,
   Algorithmic Graph Theory,
   Cambridge University Press, 1985.
6. John Hartigan, M A Wong,
   Algorithm AS 136: A K-Means Clustering Algorithm,
   Applied Statistics,
   Volume 28, Number 1, 1979, pages 100-108.
7. Barry Joe,
   GEOMPACK - a software package for the generation of meshes using geometric algorithms,
   Advances in Engineering Software,
   Volume 13, pages 325-331, 1991.
8. Hang Tong Lau,
   Algorithms on Graphs,
   Tab Books, 1989.
9. Atsuyuki Okabe, Barry Boots, Kokichi Sugihara, Sung Nok Chiu,
   Spatial Tesselations: Concepts and Applications of Voronoi Diagrams,
   Second Edition,
   Wiley, 2000.
10. Joseph O'Rourke,
    Computational Geometry,
    Cambridge University Press,
    Second Edition, 1998.
11. Helmut Spaeth,
    Cluster Analysis Algorithms for Data Reduction and Classification of Objects,
    Ellis Horwood, 1980.
12. David Sparks,
    Algorithm AS 58: Euclidean Cluster Analysis,
    Applied Statistics,
    Volume 22, Number 1, 1973,
    pages 126-130.

Source Code:

• cities.f90, the source code.
• cities.csh, commands to compile the source code.

Examples and Tests:

• cities_prb.f90, a sample problem.
• cities_prb.csh, commands to compile and run the problem.
• cities_prb_output.txt, the output file.

List of Routines:

• CH_CAP capitalizes a single character.
• CH_EQI is a case insensitive comparison of two characters for equality.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• DIST_PRINT prints the distance matrix.
• DIST_READ reads a distance matrix from a file.
• DIST_WRITE writes a distance matrix to a file.
• DMS_PRINT prints the latitude and longitude in degrees/minutes/seconds.
• DMS_READ reads DMS data from a file.
• DMS_TO_DIST creates a distance matrix from latitudes and longitudes.
• DMS_TO_DISTANCE_EARTH finds the distance between two points on the earth.
• DMS_TO_RADIANS converts degrees, minutes, seconds to radians.
• DMS_TO_XY creates pseudo X,Y coordinates from latitudes and longitudes.
• DMS_WRITE writes a latitude, longitude file.
• GET_UNIT returns a free FORTRAN unit number.
• I4_SIGN evaluates the sign of an I4.
• I4_TO_A returns the I-th alphabetic character.
• LAT_CHAR returns a character for negative or positive latitude.
• LONG_CHAR returns a character for negative or positive longitude.
• MAIN_READ_CODE reads the name of the code file from the main file.
• MAIN_READ_DIST reads the name of the distance file from the main file.
• MAIN_READ_DMS reads the name of the DMS file from the main file.
• MAIN_READ_GEOM reads the name of the geometry from the main file.
• MAIN_READ_NAME reads the name of the name file from the main file.
• MAIN_READ_SIZE reads the problem size N from the main file.
• MAIN_READ_WEIGHT reads the name of the weight file from the main file.
• MAIN_READ_XY reads the name of the XY file from the main file.
• POINTS_DIST_SPHERE finds the distance between two points on a sphere.
• R8MAT_PRINT prints an R8MAT, with an optional title.
• R8VEC_PRINT prints a real vector.
• S_EQI is a case insensitive comparison of two strings for equality.
• S_REP_ONE replaces the first occurrence of SUB1 with SUB2.
• S_TO_I4 reads an I4 from a string.
• S_TO_R8 reads an R8 from a string.
• S_TO_W reads the next blank-delimited word from a string.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• WORD_COUNT counts the number of "words" in a string.
• WORD_NEXT_READ "reads" words from a string, one at a time.
• WEIGHT_READ reads weights from a file.
• XY_PRINT prints XY planar locations.
• XY_READ reads XY planar locations from a file.
• XY_TO_DIST creates a distance matrix from a list of (X,Y) plane positions.
• XY_WRITE writes XY coordinates to a file.

You can go up one level to the FORTRAN90 source codes.