Persistence-sensitive simpli cation of functions on surfaces in linear time

Persistence provides a way of grading the importance of homological features in the sublevel sets of a real-valued function. Following the de nition given by Edelsbrunner, Morozov and Pascucci, an ε-simpli cation of a function f is a function g in which the homological noise of persistence less than ε has been removed. In this paper, we give an algorithm for constructing an ε-simpli cation of a function de ned on a triangulated surface in linear time. Our algorithm is very simple, easy to implement and follows directly from the study of the ε-simpli cation of a function on a tree. We also show that the computation of persistence de ned on a graph can be performed in linear time in a RAM model. This gives an overall algorithm in linear time for both computing and simplifying the homological noise of a function f on a surface. ∗Gipsa-Lab, CNRS UMR 5216, Grenoble, France. [email protected] †INRIA Sophia Antipolis Méditerranée, France. [email protected] ‡Duke University. [email protected]