Approximate Dynamic Programming using Halfspace Queries and Multiscale Monge Decomposition

Abstract

We consider the problem of approximating a signal P with another signal F consisting of a few piecewise constant segments. This problem arises naturally in applications including databases (e.g., histogram construction), speech recognition, computational biology (e.g., denoising aCGH data) and many more. Specifically, let P = (P1, P2,..., Pn), Pi ∈ R for all i, be a signal and let C be a constant. Our goal is to find a function F: [n] → R which optimizes the following objective function: (0.1) min F n