Voronoi diagrams have several important applications in science and engineering. While the properties and algorithms for the ordinary Voronoi diagram of point set have been well-known, their counterparts for a set of spheres have not been sufficiently studied. In this paper, we present the definition, properties and algorithms for the Voronoi diagram of 3D spheres based on the Euclidean distanc...

This paper revisits the k-nearest-neighbor (k-NN) Voronoi diagram and presents the first output-sensitive paradigm for its construction. It introduces the k-NN Delaunay graph, which corresponds to the graph theoretic dual of the k-NN Voronoi diagram, and uses it as a base to directly compute the k-NN Voronoi diagram in R. In the L1, L∞ metrics this results in O((n + m) log n) time algorithm, us...

k-median and k-center are two well-known problems in facility location which play an important role in operation research, management science, clustering and computational geometry. To the best of our knowledge, although these problems have lots of applications, they have never been studied together simultaneously as a multi objective optimization problem. Multi-objective optimization has been ...

This paper concerns the behavior of an SINR diagram of wireless systems, composed of a set S of n stations embedded in R, when restricted to the corresponding Voronoi diagram imposed on S. The diagram obtained by restricting the SINR zones to their corresponding Voronoi cells is referred to hereafter as an SINR+Voronoi diagram. The study of SINR+Voronoi diagrams is motivated by the following tw...

The ordinary point Voronoi diagram is a partition of the plane, in the way that each object (point) partitions the euclidean plane into a region, that is the locus of points which are closer from that object than from any other object (see Preparata and Shamos [7]). The Voronoi diagram has many applications in a variety of disciplines, and has been widely treated in the literature (see Okabe an...

This paper proposes an algorithm for simplifying point features on maps based on the multiplicatively weighted Voronoi diagram (MWVD). To ensure statistical, thematic, metric, and topological information contained in the original point features can be transmitted correctly after simplification, the algorithm selects corresponding measures to quantify these four types of information, and integra...

In this paper, we propose a novel image steganographic technique based on the Voronoi diagram. The basic idea is to generate a Voronoi diagram of a graph transformed from cover image; that is, the Voronoi points correspond to every two consecutive pixels in the cover image. According to the secret bits to be embedded, every Voronoi point will either be replaced by one of its neighbors or keep i...

In this paper, we present an obstacle avoiding path planning method based on Voronoi diagram and composite Bezier curve algorithm which obtains the shortest path length. In our algorithm, a Voronoi diagram is constructed according to the global environment. The piecewise linear rough path in the Voronoi diagram which keeps away from the obstacles is obtained by performing Dijkstra’s shortest pa...

We extend the Voronoi diagram framework to compute the critical area of a circuit layout [15, 12, 16, 13, 14] with the ability to accurately compute critical area for via-blocks on via and contact layers in the presence of multilayer loops, redundant vias, and redundant interconnects. Critical area is a measure reflecting the sensitivity of a VLSI design to random defects during IC manufacturin...

Details of algorithms to construct the Voronoi diagrams and medial axes of planars domain bounded by free-form (polynomial or rational) curve segments are presented, based on theoretical foundations given in the rst installment Ramamurthy and Farouki, J. Comput. Appl. Math. (1999) 102 119–141 of this two-part paper. In particular, we focus on key topological and computational issues that arise ...