Largest Empty Circle Research Articles

The largest empty circle with location constraints in spatial databases

Given a set S of points in the two-dimensional space, which are stored in a spatial database, this paper presents an efficient algorithm to find, in the area delimited by those points, the empty circle with the largest area that contains only a query point q. Our algorithm adapts previous work in the field of computational geometry to be used in spatial databases, which requires 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 efficiency and scalability by running a set of experiments using both synthetic and real data.

The Quality of Sampling from Geographic Networks

We empirically investigate the factors affecting the quality of information obtained by randomly sampling nodes from a network embedded in two-dimensional space. The motivation for this work is that wireless and other physical networks do in fact have embedding of their nodes in space, although analyses of random walks on such networks often only consider the link structure while ignoring node locations. Of independent interest is the measure we propose to evaluate the quality of sampling: the rate of decrease in the area of the largest empty circle remaining.

PENENTUAN LOKASI SMA NEGERI MENGGUNAKAN DIAGRAM VORONOI BERBOBOT DI KOTA DENPASAR

In school development problem, determining location is one of important things to consider. In this research, the purpose is to determine the location of SMAN 9 Denpasar if it will be built. One of algorithms in computational geometry that can be used to find solution of facility location problem is multiplicatively weighted Voronoi diagram in two dimensions. The result of weighted Voronoi diagram shows the influence of each site to the surrounding area. Then, the location of SMAN 9 Denpasar is obtained by determining the center of the largest empty circle of the weighted Voronoi diagram.

Semi-Online Maintenance of Geometric Optima and Measures

We give the first nontrivial worst-case results for dynamic versions of various basic geometric optimization and measure problems under the semi-online model, where during the insertion of an object we are told when the object is to be deleted. Problems that we can solve with sublinear update time include the Hausdorff distance of two point sets, discrete 1-center, largest empty circle, convex hull volume in three dimensions, volume of the union of axis-parallel cubes, and minimum enclosing rectangle. The decision versions of the Hausdorff distance and discrete 1-center problems can be solved fully dynamically. Some applications are mentioned.

Parallel geometric algorithms on a mesh-connected computer

We show that a number of geometric problems can be solved on a √n × √n mesh-connected computer (MCC) inO(√n) time, which is optimal to within a constant factor, since a nontrivial data movement on an MCC requires Ω(√n) time. The problems studied here include multipoint location, planar point location, trapezoidal decomposition, intersection detection, intersection of two convex polygons, Voronoi diagram, the largest empty circle, the smallest enclosing circle, etc. TheO(√n) algorithms for all of the above problems are based on the classical divide-and-conquer problem-solving strategy.