Computing the Closest Point to a Circle

In this paper we consider the problem of computing the closest point to the boundary of a circle among a set S of n points. We present two algorithms to solve this problem. One algorithm runs in O(n3 ) preprocessing time and space and O(log2 n) query time. The other algorithm runs in O(n1+ ) preprocessing time and O(n log n) space and O(n2/3+ ) query time. Thus we exhibit a trade-off between preprocessing and query times For dimensions d ≥ 3 we present an algorithm with O(n d/2 + ) preprocessing time to report an approximate closest point to the boundary of d-dimensional query sphere R in O(n1−1/(d+1)+ ) query time.

• Type: Conference
• Year: 2003
• Where: CCCG
• Authors: Pinaki Mitra, Asish Mukhopadhyay, S. V. Rao
• Keywords: Algorithm, CCCG 2003, CCCG 2007, Preprocessing, Query Time