Online Uniformly Inserting Points on Grid
نویسندگان
چکیده
In this paper, we consider the problem of inserting points in a square grid, which has many background applications, including halftone in reprographic and image processing. We consider an online version of this problem, i.e., the points are inserted one at a time. The objective is to assign the points as uniform as possible. Precisely speaking, after each insertion, the gap ratio should be as small as possible. In this paper, we give an insertion strategy with the maximal gap ratio no more than 2 √ 2 ≈ 2.828, which is the first result on uniformly inserting point on grid. Moreover, we show that no online algorithm can achieve the maximal gap ratio strictly less than 2.5 for a 3× 3 grid.
منابع مشابه
Online Inserting Points Uniformly on the Sphere
In many scientific and engineering applications, there are occasions where points need to be inserted uniformly onto a sphere. Previous works on uniform point insertion mainly focus on the offline version, i.e., to compute N positions on the sphere for a given interger N with the objective to distribute these points as uniformly as possible. An example application is the Thomson problem where t...
متن کاملIncremental construction along space-filling curves
For the incremental construction of a Delaunay triangulation, we prove that inserting points in rounds and walking along a space-filling curve in each round yields an algorithm running in linear expected time for uniformly distributed points. We complement this result by a simpler incremental construction running in linear expected time in any dimension.
متن کاملOn some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces
In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...
متن کاملStrong convergence results for fixed points of nearly weak uniformly L-Lipschitzian mappings of I-Dominated mappings
In this paper, we prove strong convergence results for a modified Mann iterative process for a new class of I- nearly weak uniformly L-Lipschitzian mappings in a real Banach space. The class of I-nearly weak uniformly L-Lipschitzian mappings is an interesting generalization of the class of nearly weak uniformly L-Lipschitzian mappings which inturn is a generalization of the class of nearly unif...
متن کاملAn Analysis of a Uniformly Accurate Difference
It will be proven that an exponential tridiagonal difference scheme, when applied with a uniform mesh of size h to: euxx + b(x)ux « fix) for 0 < x < 1, b > 0, b and / smooth, e in (0, 1], and u(0) and u(\) given, is uniformly second-order accurate (i.e., the maximum of the errors at the grid points is bounded by Ch2 with the constant C independent of h and e). This scheme was derived by El-Mist...
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:
دوره شماره
صفحات -
تاریخ انتشار 2010