The largest empty circle with location constraints in spatial databases

Abstract

Given a set S of points in the two-dimensional space, which are stored in a spatial database, this paper presents an e cient algorithm to nd the empty circle, in the area delimited by those points, with the largest area and containing only a query point q. Our algorithm adapts previous work in the eld of computational geometry to be used in spatial databases, which require to manage large amounts of data. To achieve this objective, the basic idea is to discard a large part of the points of S, in such a way that the problem can be solved providing only the remaining points to a classical computational geometry algorithm that, by processing a smaller collection of points, saves main memory resources and computation time. The correctness of our algorithm is formally proven. In addition, we empirically show its e ciency and scalability by running a set of experiments using both synthetic and real data.