test_nearest, a FORTRAN90 code which tests several functions that carry out the nearest neighbor calculation.

In a nearest neighbor calculation, we are given:

  • R, a set of NR points in M dimensions.
  • S, a set of NS points in M dimensions.
  • D(x,y), a norm for measuring distances between points in M dimensions.
  • and we are asked to compute, for each point S(JS),

    Obviously, one method to determine the values in NEAREST is simply to compute every distance and take the index of the minimum. But even this simple idea can be implemented in many ways in MATLAB, and implementations will vary in their cost in memory and time.

    Also, note that if the dimension M is small, and if the size of the R set is small relative to that of S, it may be much cheaper to compute the Delaunay triangulation of R (or its higher-dimensional generalization). Computing the triangulation is somewhat expensive, but makes the search procedure extremely quick.

    Lloyd's version of the Centroidal Voronoi Tessellation (CVT) algorithm estimates the area or volume of the cells using sampling. This computation is a nearest neighbor calculation.


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


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

    Related Programs:

    CVT, a FORTRAN90 code which computes elements of a Centroidal Voronoi Tessellation (CVT).

    NEAREST_INTERP_1D, a FORTRAN90 code which interpolates a set of data using a piecewise constant interpolant defined by the nearest neighbor criterion.



    1. Sunil Arya, David Mount, Nathan Netanyahu, Ruth Silverman, Angela Wu,
      An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions,
      Journal of the ACM,
      Volume 45, Number 6, November 1998, pages 891-923.
    2. Jon Bentley, Bruce Weide, Andrew Yao,
      Optimal Expected Time Algorithms for Closest Point Problems,
      ACM Transactions on Mathematical Software,
      Volume 6, Number 4, December 1980, pages 563-580.
    3. Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
      Computational Geometry,
      Springer, 2000,
      ISBN: 3-540-65620-0,
      LC: QA448.D38.C65.

    Source Code:

    Last revised on 03 September 2020.