Maximizing a Voronoi Region: The Convex Case
نویسندگان
چکیده
Given a set S of s points in the plane, where do we place a new point, p, in order to maximize the area of its region in the Voronoi diagram of S and p? We study the case where the Voronoi neighbors of p are in convex position, and prove that there is at most one local maximum.
منابع مشابه
Dilation, smoothed distance, and minimization diagrams of convex functions
Clarkson recently introduced the o-smoothed distance do(p,q) = 2d(p,q)/(d(o, p)+d(o,q)+d(p,q)) (where d denotes the Euclidean distance in the plane) as a geometric analogue of the Jaccard distance; its Voronoi diagrams can be used to determine for a query point q the site p maximizing the dilation (d(p,o)+d(o,q))/d(p,q) of p and q in a star network centered at o. Although smoothed distance is n...
متن کاملOn the Average Complexity of 3D-Voronoi Diagrams of Random Points on Convex Polytopes
It is well known that the complexity, i.e. the number of vertices, edges and faces, of the 3-dimensional Voronoi diagram of n points can be as bad as (n2). It is also known that if the points are chosen Independently Identically Distributed uniformly from a 3-dimensional region such as a cube or sphere, then the expected complexity falls to O(n). In this paper we introduce the problem of analyz...
متن کاملOn Some Optimization Problems in Obnoxious Facility Location
In this paper we study the following general MaxMinoptimization problem concerning undesirable (obnoxious) facility location: Given a set of n sites S inside a convex region P , construct m garbage deposit sites Vm such that the minimum distance between these sites Vm and the union of S and Vm, Vm∪S, is maximized. We present a general method using Voronoi diagrams to approximately solve two suc...
متن کاملOn the Hausdorff and Other Cluster Voronoi Diagrams
The Voronoi diagram is a fundamental geometric structure that encodes proximity information. Given a set of geometric objects, called sites, their Voronoi diagram is a subdivision of the underlying space into maximal regions, such that all points within one region have the same nearest site. Problems in diverse application domains (such as VLSI CAD, robotics, facility location, etc.) demand var...
متن کاملVoronoi Cells of Lattices with Respect to Arbitrary Norms
Motivated by the deterministic single exponential time algorithm of Micciancio and Voulgaris for solving the shortest and closest vector problem for the Euclidean norm, we study the geometry and complexity of Voronoi cells of lattices with respect to arbitrary norms. On the positive side, we show that for strictly convex and smooth norms the geometry of Voronoi cells of lattices in any dimensio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Int. J. Comput. Geometry Appl.
دوره 15 شماره
صفحات -
تاریخ انتشار 2002