Efficient Algorithms for Approximating Polygonal Chains

We consider the problem of approximating a polygonal chain C by another polygonal chain C whose vertices are constrained to be a subset of the set of vertices of C. The goal is to minimize the number of vertices needed in the approximation C . Based on a framework introduced by Imai and Iri [25], we define an error criterion for measuring the quality of an approximation. We consider two problems. (1) Given a polygonal chain C and a parameter 0, compute an approximation of C, among all approximations whose error is at most , that has the smallest number of vertices. We present an O(n4/3+ )-time algorithm to solve this problem, for any > 0; the constant of proportionality in the running time depends on . (2) Given a polygonal chain C and an integer k, compute an approximation of C with at most k vertices whose error is the smallest among all approximations with at most k vertices. We present a simple randomized algorithm, with expected running time O(n4/3+ ), to solve this problem....

• Type: Journal
• Year: 2000
• Where: DCG
• Authors: Pankaj K. Agarwal, Kasturi R. Varadarajan
• Keywords: Approximations, DCG 2000, Error Criterion, Polygonal Chain