Space-efficient algorithms for approximating polygonal curves in two dimensional space

Abstract

Given an n-vertexp olygonal curve P = [p1, p2, …, pn] in the 2-dimensional space R2, we consider the problem of approximating P by finding another polygonal curve Pʹ = [p ʹ 1, pʹ 2, . . ., pʹ m] of m vertices in R2 such that the vertexs equence of P ʹ is an ordered subsequence of the vertices along P. The goal is to either minimize the size m of Pʹ for a given error tolerance Є (called the min-# problem), or minimize the deviation error Є between P and Pʹ for a given size m of P ʹ (called the min-# problem). We present useful techniques and develop a number of efficient algorithms for solving the 2-D min-# and min-# problems under two commonly-used error criteria for curve approximations. Our algorithms improve substantially the space bounds of the previously best known results on the same problems while maintain the same time bounds as those of the best known algorithms.