Predicting system performance by interpolation using a high-dimensional delaunay triangulation

When interpolating computing system performance data, there are many input parameters that must be considered. Therefore, the chosen multivariate interpolation model must be capable of scaling to many dimensions. The Delaunay triangulation is a foundational technique, commonly used to perform piecewise linear interpolation in computer graphics, physics, civil engineering, and geography applications. It has been shown to produce a simplex based mesh with numerous favourable properties for interpolation. While computation of the two- and three-dimensional Delaunay triangulation is a well-studied problem, there are numerous technical limitations to the computability of a high-dimensional Delaunay triangulation. This paper proposes a new algorithm for computing interpolated values from the Delaunay triangulation without computing the complete triangulation. The proposed algorithm is shown to scale to over 50 dimensions. Data is presented demonstrating interpolation using the Delaunay triangulation in a real world high performance computing system problem.