We introduce an algorithm for computing Voronoi diagrams of points, straight-line segments and circular arcs in the two-dimensional Euclidean plane. Based on a randomized incremental insertion, we achieve a Voronoi algorithm that runs in expected time O(n log n) for a total of n points, segments and arcs, if at most a constant number of segments and arcs is incident upon every point. Our theore...

Our goal in this paper is to examine the application of Voronoi diagrams, a fundamental concept of computational geometry, to the nearest neighbor algorithm used in machine learning. We consider the question “Given a planar polygonal tessellation T and an integer k, is there a set of k points whose Voronoi diagram contains every edge in T?” We show that this question is NP-hard. We encountered ...

Several studies have exploited the properties of Voronoi diagrams to improve variations of the nearest neighbor search on stored datasets. However, the significance of Voronoi diagrams and their basic building blocks, Voronoi cells, has been neglected when the geometry data is incrementally becoming available as a data stream. In this paper, we study the problem of Voronoi cell computation for ...

We address the problem of computing critical area for open faults in a circuit layout in the presence of multilayer loops and redundant interconnects. The extraction of critical area is a fundamental problem in VLSI yield prediction. We first model the problem as a graph problem and then we solve it efficiently by exploiting its geometric nature. We introduce the open-fault Voronoi diagram of p...