FINDING THE LARGEST EMPTY DISK CONTAINING A QUERY POINT

Abstract

Let P be a set of n points in the plane. We present an efficient algorithm for preprocessing P, so that, for a given query point q, we can quickly report the largest disk that contains q but its interior is disjoint from P. The storage required by the data structure is O(n log n), the preprocessing cost is O(n log 2 n), and a query takes O( log 2 n) time. We also present an alternative solution with an improved query cost and with slightly worse storage and preprocessing requirements.