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  5. DELAUNAYSPARSE contains both serial and parallel codes written in Fortran 2003 (with OpenMP) for performing medium- to high-dimensional interpolation via the Delaunay triangulation. To accommodate the exponential growth in the size of the Delaunay triangulation in high dimensions, DELAUNAYSPARSE computes only a sparse subset of the complete Delaunay triangulation, as necessary for performing interpolation at the user specified points. This article includes algorithm and implementation details, complexity and sensitivity analyses, usage information, and a brief performance study.