Fitting a graph to one-dimensional data

Abstract

Given n data points in R-d , an appropriate edge-weighted graph connecting the data points finds application in solving clustering, classification, and regression problems. The graph proposed by Daitch, Kelner and Spielman (ICML 2009) can be computed by quadratic programming and hence in polynomial time. While a more efficient algorithm would be preferable, replacing quadratic programming is challenging even for the special case of points in one dimension. We develop a dynamic programming algorithm for this case that runs in O(n(2)) time under the Real-RAM model, where arithmetic on real numbers takes constant time. (C) 2021 Elsevier B.V. All rights reserved.