基于Voronoi图的组最近邻查询

组最近邻查询由于涉及多个查询点,因此比传统的最近邻查询更为复杂.充分考虑查询点的分布特征以及它们构成的几何图形的性质和特点,给出组最近邻所应满足的条件及判断组最近邻的理论方法.提出基于Voronoi图的组最近邻查询的VGNN算法,可以精确求解查询点集的最近邻.对于查询点不共线的情况,该算法的查询方式是以一点为中心、向外扩张式的;对于查询点共线的情况,该算法给出搜索范围,限定了参与计算的数据点的个数.给出基于Voronoi图的VTree索引.实验结果表明,基于VTree索引的VGNN算法具有较好的性能,并且当查询点不共线时,其性能具有较高的稳定性.     

Weight-proportional Space Partitioning Using Adaptive Voronoi Diagrams

Traditional application of Voronoi diagrams for space partitioning results in Voronoi regions, each with a specific area determined by the generators’ relative locations and weights. Particularly in the area of information space (re)construction, however, there is a need for inverse solutions; i.e., finding weights that result in regions with predefined area ratios. In this paper, we formulate an adaptive Voronoi solution and propose a raster-based optimization method for finding the associated weight set. The solution consists of a combination of simple, fixed-point iteration with an optional spatial resolution refinement along the regions’ boundaries using quadtree decomposition. We present the corresponding algorithm and its complexity analysis. The method is successfully tested on a series of ideal–typical cases and the interactions between the adaptive technique and boundary resolution refinement are explored and assessed.

Approximation of Generalized Voronoi Diagrams by Ordinary Voronoi Diagrams

A numerically robust algorithm for the ordinary Voronoi diagrams is applied to the approximation of various types of generalized Voronoi diagrams. The generalized Voronoi diagrams treated here include Voronoi diagrams for figures, additively weighted Voronoi diagrams, Voronoi diagrams in a river, Voronoi diagrams in a Riemannian plane, and Voronoi diagrams with respect to collision-avoiding shortest paths. The construction of these generalized Voronoi diagrams is reduced to the construction of the ordinary Voronoi diagrams. The methods proposed here can save much time which is otherwise necessary for writing a computer program for each type of generalized Voronoi diagram.     

基于Voronoi图的最近邻查询的研究

移动查询点的最近邻查询是移动计算和现实生活应用中一种很基本也很重要的查询类型.基于Voronoi图的最近邻查询在计算几何中已被研究了相当长一段时间.但在以往的研究中基于Voronoi图的最近邻查询究竟是基于何种具体的索引结构去实现对查询空间的搜索的,却很少被提及.本文把传统的R树和Voronoi图在解决最近邻查询问题中的优越性相结合,提出了一种新的索引结构:VR树.进而给出了基于VR树索引结构的1NN查询算法.     

基于障碍物群的k全局相异最优有序路径查询

提出障碍k全局相异最优有序路径的查询问题,利用可视图的思想给出近似查询算法,通过作用集与障碍角度点的引入有效地减少构造可视图障碍对象的数量,分析查询点和数据点构成的线段与可视图的顶点和弧的关系,减少内部障碍路径的计算次数,实现算法的全面优化。实验结果表明,该算法具有较好的性能。     

An Optimal Algorithm for Processing Distributed Star Queries

The problem of optimal query processing in distributed database systems was shown to be NP-hard. However, for a special type of queries called star queries, we have developed a polynomial optimal algorithm. Semijoin tactics are applied for query processing. An execution graph is introduced to represent the semijoin programs associated with the distributed processing of the queries. We then identify optimality properties of semijoin programs for star queries, and use these properties to derive the optimal semijoin program. We have shown that the optimal semijoin program can be found from serial semijoin strategies, defined as serial semijoin programs which include each semijoin associated with the query exactly once. By making certain assumptions on the file sizes and the semijoin selectivities, we can obtain the optimal semijoin program from these strategies in polynomial time. Our assumption on selectivites is consistent in the sense that we consider the selectivity of a semijoin based on the current database state, i.e., we take into consideration the reduction effects of all prior semijoins.     

Enclosing Surfaces for Point Clusters Using 3D Discrete Voronoi Diagrams

Point clusters occur in both spatial and non-spatial data. In the former context they may represent segmented particle data, in the latter context they may represent clusters in scatterplots. In order to visualize such point clusters, enclosing surfaces lead to much better comprehension than pure point renderings.
We propose a flexible system for the generation of enclosing surfaces for 3D point clusters. We developed a GPU-based 3D discrete Voronoi diagram computation that supports all surface extractions. Our system provides three different types of enclosing surfaces. By generating a discrete distance field to the point cluster and extracting an isosurface from the field, an enclosing surface with any distance to the point cluster can be generated. As a second type of enclosing surfaces, a hull of the point cluster is extracted. The generation of the hull uses a projection of the discrete Voronoi diagram of the point cluster to an isosurface to generate a polygonal surface. Generated hulls of non-convex clusters are also non-convex. The third type of enclosing surfaces can be created by computing a distance field to the hull and extracting an isosurface from the distance field. This method exhibits reduced bumpiness and can extract surfaces arbitrarily close to the point cluster without losing connectedness.
We apply our methods to the visualization of multidimensional spatial and non-spatial data. Multidimensional clusters are extracted and projected into a 3D visual space, where the point clusters are visualized. The respective clusters can also be visualized in object space when dealing with multidimensional particle data.     

利用自动机高效处理XML路径表达式查询

在XML查询处理中,应用于绝大多数XML查询语言中的路径表达式在定位和查询XML数据和数据的结构关系方面具有极强的表达能力,并且由于XML数据的半结构化性,使得XML路径表达式查询的查询处理技术的研究与传统的数据库查询处理技术相比有着全新的特点和挑战.一些目前已有的查询处理技术可以用来处理路径表达式,但是查询处理中产生的大量中间结果导致了这些方法应用在大规模XML文档和复杂的路径表达式查询中时查询效率急剧下降.文中利用自动机技术设计了一个处理XML路径表达式查询的高效方法--SAM.SAM的基本思想是将路径表达式查询转化成一个与之完全等价的自动机,然后将其与从XML文档中抽象出来的模式路径相匹配.文中同时也给出了基于SAM方法的针对路径表达式中"//"操作符计算的有效解决方案.实验证明:SAM是一种非常有效的查询方法,在计算大数据量复杂路径表达式查询时具有非常高的效率,是一种实用的XML路径表达式查询方法.     

On Voronoi Diagrams and Medial Axes

Medial axes and Voronoi diagrams stand among the most influencing ideas in computer vision and image analysis. Relationships between them, with respect to polygons, had been noted decades ago, and recently this was extended for a broader class of shapes. More specifically, Voronoi diagrams have been considered as a means through which optimal computational geometry algorithms can be applied for performing symmetry axis calculation. This paper is aimed at establishing a closer theoretical relation between Voronoi diagrams and medial axes. Extensions of the definitions of these concepts are proposed, and the advantages of these definitions with respect to some specific but relevant cases are highlighted. In addition, medial axes are characterized as a particular case of Voronoi diagrams, and the implications of this fact are discussed.     

Planar Minimization Diagrams via Subdivision with Applications to Anisotropic Voronoi Diagrams

Let X = {f₁, …, f_n} be a set of scalar functions of the form f_i : ?² → ? which satisfy some natural properties. We describe a subdivision algorithm for computing a clustered ε‐isotopic approximation of the minimization diagram of X. By exploiting soft predicates and clustering of Voronoi vertices, our algorithm is the first that can handle arbitrary degeneracies in X, and allow scalar functions which are piecewise smooth, and not necessarily semi‐algebraic. We apply these ideas to the computation of anisotropic Voronoi diagram of polygonal sets; this is a natural generalization of anisotropic Voronoi diagrams of point sites, which extends multiplicatively weighted Voronoi diagrams. We implement a prototype of our anisotropic algorithm and provide experimental results.     

Dynamic Rematerialization: Processing Distributed Queries Using Redundant Data

In this paper an approach to processing distributed queries that makes explicit use of redundant data is proposed. The basic idea is to focus on the dynamics of materialization, defined as the collection of data and partial results available for processing at any given time, as query processing proceeds. In this framework the role of data redudancy in maximizing parallelism and minimizing data movement is clarified. What results is not only the discovery of new algorithms but an improved framework for their evaluation.     

基于改进蚁群算法的多无人机航路规划研究

无人机的航路规划研究是无人机任务控制系统的关键技术,在用Voronoi图法对威胁环境建模的摹础上,提出了基于Voronoi图的多行为蚁群算法,增强了蚂蚁之间的协同性,有效解决了可行解的收敛性与多样性之间的矛盾,并对求解过程加入了方向性引导,提高了算法的求解效率.在多机协同方面,利用上述算法分同起止点与不同起止点两种情况对多机协同航路规划进行了仿真,针对得到的多条初始航路,利用协同时间指标对多初始航路进行选择.最后用三次样条方法对协同最优航路进行了平滑处理.     

基于Voronoi图的线段最近对查询

最近对查询是空间数据库中的重要查询之一。已有的关于最近对查询的研究基本集中在点对象上,对空间对象无法抽象为点的对象则研究较少。提出基于平面线段的最近对查询,即找出两个平面线段集中距离最近的线段对。提出基于Voronoi图的线段最近对查询算法,该方法构造两个线段集的Voronoi图,利用Voronoi图的最近邻近特性和局域动态特性找到互为最近邻的线段对,从中找到结果,以缩减大量的计算代价。对线段集中增加线段和删除线段的情况做了相应的处理。实验证明,该算法具有较高的查询效率。     

Approximated Centroidal Voronoi Diagrams for Uniform Polygonal Mesh Coarsening

We present a novel clustering algorithm for polygonal meshes which approximates a Centroidal Voronoi Diagram construction. The clustering provides an efficient way to construct uniform tessellations, and therefore leads to uniform coarsening of polygonal meshes, when the output triangulation has many fewer elements than the input mesh. The mesh topology is also simplified by the clustering algorithm. Based on a mathematical framework, our algorithm is easy to implement, and has low memory requirements. We demonstrate the efficiency of the proposed scheme by processing several reference meshes having up to 1 million triangles and very high genus within a few minutes on a low‐ end computer.     

Diffusion Diagrams: Voronoi Cells and Centroids from Diffusion

We define Voronoi cells and centroids based on heat diffusion. These heat cells and heat centroids coincide with the common definitions in Euclidean spaces. On curved surfaces they compare favorably with definitions based on geodesics: they are smooth and can be computed in a stable way with a single linear solve. We analyze the numerics of this approach and can show that diffusion diagrams converge quadratically against the smooth case under mesh refinement, which is better than other common discretization of distance measures in curved spaces. By factorizing the system matrix in a preprocess, computing Voronoi diagrams or centroids amounts to just back‐substitution. We show how to localize this operation so that the complexity is linear in the size of the cells and not the underlying mesh. We provide several example applications that show how to benefit from this approach.     

二维黎曼流形的Voronoi图生成算法

提出采用黎曼流形描述研究对象和基于坐标卡生成Voronoi图的算法思路.讨论了黎曼流形上研究Voronoi图的难点,并给出了存在定理,该定理说明了坐标卡上Voronoi图的存在条件.按照算法思路和存在定理,详细描述了二维黎曼流形上创建坐标卡的算法,并给出流形上转换函数和混合函数的定义方法.最后描述了基于坐标卡生成Voronoi图的算法,并给出了具体实例.     

On 2-Site Voronoi Diagrams Under Geometric Distance Functions

We revisit a new type of Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, namely, circles and triangles, and analyze the structure and complexity of the nearest- and furthest-neighbor 2-site Voronoi diagrams of a point set in the plane with respect to these distance functions. In addition, we bring to notice that 2-point site Voronoi diagrams can be alternatively interpreted as 1-site Voronoi diagrams of segments, and thus, our results also enhance the knowledge on the latter.