Fully Dynamic Geometric Spanners

In this paper we present an algorithm for maintaining a spanner over a dynamic set of points in constant doubling dimension metric spaces. For a set S of points in ? ^d , a t-spanner is a sparse graph on the points of S such that there is a path in the spanner between any pair of points whose total length is at most t times the distance between the points. We present the first fully dynamic algorithm for maintaining a spanner whose update time depends solely on the number of points in S. In particular, we show how to maintain a (1+ε)-spanner with O(n/ε ^d ) edges, where points can be inserted to S in an amortized update time of O(log?n) and deleted from S in an amortized update time of $\tilde{O}(n^{1/3})$ . As a by-product of our techniques we obtain a simple incremental algorithm for constructing a (1+ε)-spanner with O(n/ε ^d ) edges in constant doubling dimension metric spaces whose running time is O(nlog?n).     

图象特征点集配准的加权相关迭代算法

图象配准是计算机视觉中目标识别的一种基本方法 .其目的是在待识别图象中寻找与模型图象的最佳匹配 .该文以传统的 U meyam a点集相关度量为基础 ,结合 Procrustes正规化方法 ,通过引入加权矩阵 ,以得到新的相关度量函数 ,进而提出了一种图象特征点集匹配的新方法 ,解决了传统方法要求点集维数相同的缺点 .经过迭代运算 ,对存在几何失真 ,且维数不同的两点集可得到精确配准 .文中给出的点集配准结果说明 ,当两点集维数相同时 ,该方法不仅与传统的点集相关法一样 ,均可达到精确配准 ,而且该方法对维数不同的点集也可实现精确配准     

The Geometric Dilation of Finite Point Sets

Let G be an embedded planar graph whose edges may be curves. For two arbitrary points of G, we can compare the length of the shortest path in G connecting them against their Euclidean distance. The supremum of all these ratios is called the geometric dilation of G. Given a finite point set, we would like to know the smallest possible dilation of any graph that contains the given points. In this paper we prove that a dilation of 1.678 is always sufficient, and that π/2 = 1.570... is sometimes necessary in order to accommodate a finite set of points.     

Near-Linear Approximation Algorithms for Geometric Hitting Sets

Given a range space $(X,\mathcal{R})$ , where $\mathcal{R}\subset2^{X}$ , the hitting set problem is to find a smallest-cardinality subset H?X that intersects each set in $\mathcal{R}$ . We present near-linear-time approximation algorithms for the hitting set problem in the following geometric settings: (i)? $\mathcal{R}$ is a set of planar regions with small union complexity. (ii)? $\mathcal{R}$ is a set of axis-parallel d-dimensional boxes in ? ^d . In both cases X is either the entire ? ^d , or a finite set of points in ? ^d . The approximation factors yielded by the algorithm are small; they are either the same as, or within very small factors off the best factors known to be computable in polynomial time.     

Spherical Fibonacci Point Sets for Illumination Integrals

Quasi‐Monte Carlo (QMC) methods exhibit a faster convergence rate than that of classic Monte Carlo methods. This feature has made QMC prevalent in image synthesis, where it is frequently used for approximating the value of spherical integrals (e.g. illumination integral). The common approach for generating QMC sampling patterns for spherical integration is to resort to unit square low‐discrepancy sequences and map them to the hemisphere. However such an approach is suboptimal as these sequences do not account for the spherical topology and their discrepancy properties on the unit square are impaired by the spherical projection. In this paper we present a strategy for producing high‐quality QMC sampling patterns for spherical integration by resorting to spherical Fibonacci point sets. We show that these patterns, when applied to illumination integrals, are very simple to generate and consistently outperform existing approaches, both in terms of root mean square error (RMSE) and image quality. Furthermore, only a single pattern is required to produce an image, thanks to a scrambling scheme performed directly in the spherical domain.     

权重模糊粗糙集的分类规则挖掘算法

针对粗糙集分类规则挖掘算法LEM2剪枝条件过于严格的问题,提出一种权重模糊粗糙集的改进规则挖掘算法。在用例带权重的模糊粗糙集理论框架上分析面向混合数据的分类规则挖掘算法,引入粗糙集模型的近似覆盖参数作为挖掘算法的泛化度量参数,实现对规则集数量和规则形式复杂程度的调节。实验结果表明,与LEM2算法和DataSqueezer算法相比,该算法的平均精度和平均召回率更优,分别为81%和80%,且生成规则的平均长度最短。     

Spanners for bounded tree-length graphs

This paper concerns construction of additive stretched spanners with few edges for n$n$-vertex graphs having a tree-decomposition into bags of diameter at most δ$\delta$, i.e., the tree-length δ$\delta$ graphs. For such graphs we construct additive 2δ$2\delta$-spanners with O(δn+nlogn)$O(\delta n+nlogn)$ edges, and additive 4δ$4\delta$-spanners with O(δn)$O\left(\delta n\right)$ edges. This provides new upper bounds for chordal graphs for which δ=1$\delta =1$. We also show a lower bound, and prove that there are graphs of tree-length δ$\delta$ for which every multiplicative δ$\delta$-spanner (and thus every additive (δ−1)$(\delta -1)$-spanner) requires Ω(n^1+1/Θ(δ))$\Omega \left(n^{1+1/\Theta \left(\delta \right)}\right)$ edges.     

Optimized Sub-Sampling of Point Sets for Surface Splatting

Using surface splats as a rendering primitive has gained increasing attention recently due to its potential for high‐performance and high‐quality rendering of complex geometric models. However, as with any other rendering primitive, the processing costs are still proportional to the number of primitives that we use to represent a given object. This is why complexity reduction for point‐sampled geometry is as important as it is, e.g., for triangle meshes. In this paper we present a new sub‐sampling technique for dense point clouds which is specifically adjusted to the particular geometric properties of circular or elliptical surface splats. A global optimization scheme computes an approximately minimal set of splats that covers the entire surface while staying below a globally prescribed maximum error toleranceε. Since our algorithm converts pure point sample data into surface splats with normal vectors and spatial extent, it can also be considered as a surface reconstruction technique which generates a hole‐free piecewise linearC^?1 continuous approximation of the input data. Here we can exploit the higher flexibility of surface splats compared to triangle meshes. Compared to previous work in this area we are able to obtain significantly lower splat numbers for a given error tolerance.     

Max-Stretch Reduction for Tree Spanners

A tree t-spanner T of a graph G is a spanning tree of G whose max-stretch is t, i.e., the distance between any two vertices in T is at most t times their distance in G. If G has a tree t-spanner but not a tree (t−1)-spanner, then G is said to have max-stretch of t. In this paper, we study the Max-Stretch Reduction Problem: for an unweighted graph G=(V,E), find a set of edges not in E originally whose insertion into G can decrease the max-stretch of G. Our results are as follows: (i) For a ring graph, we give a linear-time algorithm which inserts k edges improving the max-stretch optimally. (ii) For a grid graph, we give a nearly optimal max-stretch reduction algorithm which preserves the structure of the grid. (iii) In the general case, we show that it is -hard to decide, for a given graph G and its spanning tree of max-stretch t, whether or not one-edge insertion can decrease the max-stretch to t−1. (iv) Finally, we show that the max-stretch of an arbitrary graph on n vertices can be reduced to s′≥2 by inserting O(n/s′) edges, which can be determined in linear time, and observe that this number of edges is optimal up to a constant.     

A Fast Geometric Method for Defuzzification of Type-2 Fuzzy Sets

Generalized type-2 fuzzy logic systems cannot currently be used for practical problems because the amount of computation required to defuzzify a generalized type-2 fuzzy set is too large. This paper presents a new method for defuzzifing a type-2 fuzzy set. The new much faster technique is based on geometric representations and operations. The results of a real world example contained in this paper show this new approach to be over 200 000 times faster than type-reduction. We present a new method for assessing the accuracy of the membership function of a type-2 fuzzy set. This method is used to show that the new representation used by the defuzzifier is not detrimental to the accuracy of the set. We also discuss the differences between the new approach and type-reduction, identifying the origin of this massive improvement in execution speed.      

基于仿射变换模型的图象特征点集配准方法研究

图象配准是计算机视觉中目标识别的一种基本方法,其目的是在待识别图象中寻找与模型图象的最佳匹配.目前,对于图象间的变换为相似变换的情形已有闭合公式.本文则分别运用最小二乘和矩阵伪逆两种方法,对图象间的变换为仿射变换的情形进行了研究,并给出了简单的闭合公式.实验表明这种方法精确、稳定、受噪声影响小.     

逐步求精的多视角点云配准方法

针对多视角点云配准问题,本文设计了一个合理的目标函数,便于将多视角配准问题分解成多个双视角配准问题,并考虑了两个要素：1）各帧点云均具有其他所有点云所未覆盖的区域;2）基准帧点云的重要程度高于其他点云.为了求解该目标函数,本文提出了逐步求精的解决策略：根据给定的配准初值构造初始模型,依次取出基准帧以外的每帧点云,利用所提出的双视角配准算法计算该帧点云的配准参数,并修正模型,以便进一步计算后续点云的配准参数.遍历完全部点云构成一次完整的循环,多次循环后可获得精确的多视角配准结果.公开数据集上的实验结果表明,本文所提出的方法能够精确、可靠地实现多视角点云配准.     

Improved Algorithms for Constructing Fault-Tolerant Spanners

Abstract. Let S be a set of n points in a metric space, and let k be a positive integer. Algorithms are given that construct k -fault-tolerant spanners for S . If in such a spanner at most k vertices and/ or edges are removed, then each pair of points in the remaining graph is still connected by a ``short' path. First, an algorithm is given that transforms an arbitrary spanner into a k -fault-tolerant spanner. For the Euclidean metric in R ^d , this leads to an O(n log n + c ^k n) -time algorithm that constructs a k -fault-tolerant spanner of degree O(c ^k ) , whose total edge length is O(c ^k ) times the weight of a minimum spanning tree of S , for some constant c . For constant values of k , this result is optimal. In the second part of the paper, algorithms are presented for the Euclidean metric in R ^d . These algorithms construct (i) in O(n log n + k ² n) time, a k -fault-tolerant spanner with O(k ² n) edges, and (ii) in O(k n log n) time, such a spanner with O(k n log n) edges.     

Improved Algorithms for Constructing Fault-Tolerant Spanners

Let S be a set of n points in a metric space, and let k be a positive integer. Algorithms are given that construct k -fault-tolerant spanners for S . If in such a spanner at most k vertices and/ or edges are removed, then each pair of points in the remaining graph is still connected by a ``short'' path. First, an algorithm is given that transforms an arbitrary spanner into a k -fault-tolerant spanner. For the Euclidean metric in R ^d , this leads to an O(n log n + c ^k n) -time algorithm that constructs a k -fault-tolerant spanner of degree O(c ^k ) , whose total edge length is O(c ^k ) times the weight of a minimum spanning tree of S , for some constant c . For constant values of k , this result is optimal. In the second part of the paper, algorithms are presented for the Euclidean metric in R ^d . These algorithms construct (i) in O(n log n + k ² n) time, a k -fault-tolerant spanner with O(k ² n) edges, and (ii) in O(k n log n) time, such a spanner with O(k n log n) edges.     

加权K-prototype-粗糙集的航班延误等级划分研究

针对航班延误程度的评估,选取了六个衡量指标建立了航班延误等级划分模型,采用了加权k-prototypes聚类算法以及粗糙集理论形成航班延误等级划分规则,并以大型枢纽机场的航班延误数据进行实例验证.结果 表明,航班延误等级划分模型有效可行,具有较高判别精度,为建立相应的应急预案以及协同流量管理提供了有效可靠的基础依据.     

基于加权相邻关系的形状轮廓点匹配

轮廓点匹配是形状匹配的一种典型方法。在各种形变情况下,形状轮廓点的相邻关系往往比其他全局关系更稳定。本文在保持局部邻居结构的点匹配算法基础上,引入了邻居的权的概念。首先基于点到邻居的距离为每个点的邻居关系赋权,然后结合形状上下文距离把点匹配问题转化为有向属性关系图匹配问题,用松弛迭代法求解。引入邻居关系系的权,使匹配不仅保持邻居集的一致性,同时还保持邻居之间的距离相对关系。实验证明,本文方法能够提高匹配效果,加快匹配算法收敛速度。     

Relaxed Spanners for Directed Disk Graphs

Let (V,δ) be a finite metric space, where V is a set of n points and δ is a distance function defined for these points. Assume that (V,δ) has a doubling dimension d and assume that each point p∈V has a disk of radius r(p) around it. The disk graph that corresponds to V and r(?) is a directed graph I(V,E,r), whose vertices are the points of V and whose edge set includes a directed edge from p to q if δ(p,q)≤r(p). In Peleg and Roditty (Proc. 7th Int. Conf. on Ad-Hoc Networks and Wireless (AdHoc-NOW), pp. 622–633, 2008) we presented an algorithm for constructing a (1+?)-spanner of size O(n? ^?d logM), where M is the maximal radius r(p). The current paper presents two results. The first shows that the spanner of Peleg and Roditty (in Proc. 7th Int. Conf. on Ad-Hoc Networks and Wireless (AdHoc-NOW), pp. 622–633, 2008) is essentially optimal, i.e., for metrics of constant doubling dimension it is not possible to guarantee a spanner whose size is independent of M. The second result shows that by slightly relaxing the requirements and allowing a small augmentation of the radius assignment, considerably better spanners can be constructed. In particular, we show that if it is allowed to use edges of the disk graph I(V,E,r _1+? ), where r _1+? (p)=(1+?)?r(p) for every p∈V, then it is possible to get a (1+?)-spanner of size O(n/? ^d ) for I(V,E,r). Our algorithm is simple and can be implemented efficiently.     

基于Vague集的加权多目标模糊决策方法

1 引言在多目标模糊决策支持系统中,通常要在多个目标中依据有关约束条件选择最佳的目标。由于信息的不确定性,许多学者采用Fuzzy集理论来处理这类问题。Chen在文[3]中提出了采用Vague集的方法来处理模糊条件下的多目标决策问题,并讨论了加权情况下的处理方法。然而在Chen的方法中,没有定义加权情况下Vague集的运算,其加权处理是针对目标选择计分函数S的,而非Vague集;并且文[3]中的     

加权模糊粗糙约简

基于模糊粗糙集的传统约简算法的时间代价较高,在处理大规模数据时耗时过长,且在许多实际大规模数据集上存在有限时间内无法收敛等问题。因此将权重引入属性约简的定义中,其中属性权重是属性重要度的数值指标。通过构建优化问题来求解属性权重,证明了属性依赖度即是属性权重的最优解。因此,提出了基于属性权重排序的约简算法,从而大大提升了约简的速度,使得约简算法可以应用于大规模数据集,特别是高维数据集中。     

Degree-Constrained Pyramid Spanners

A t-spanner of a pyramid network is a subnetwork in which every two nodes that were connected by an edge in the original pyramid can be connected by a path in the subnetwork with at most t edges. We give several results that present trade-offs between t and the maximum degree of a t-spanner.