cities, a C++ code which works with problems involving the distance between a set of cities on a map.

Such problems include:


The computer code and data files described and made available on this web page are distributed under the MIT license


cities is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

ASA058, a C++ code which contains the original text of the Sparks clustering algorithm.

ASA136, a C++ code which implements the K-Means algorithm.

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


FLOYD, a C++ code which implements Floyd's algorithm for finding the shortest distance between pairs of nodes on a directed graph.

KMEANS, a C++ code which treats the K-means problem of grouping a discrete set of N points into K clusters.

POINT_MERGE, a C++ code which considers N points in M dimensional space, and counts or indexes the unique or "tolerably unique" items.

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

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

TSP, a dataset directory which contains test data for the traveling salesperson problem;


  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.
  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.
  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:

Last revised on 19 February 2020.