Efficient Flexible M-Tree Bulk Loading Using FastMap and Space-Filling Curves

Many database applications currently deal with objects in a metric space.Examples of such objects include unstructured multimedia objects and points of interest(POIs)in a road network.The M-tree is a dynamic index structure that facilitates an efficient search for objects in a metric space.Studies have been conducted on the bulk loading of large datasets in an M-tree.However,because previous algorithms involve excessive distance computations and disk accesses,they perform poorly in terms of their index construction and search capability.This study proposes two efficient M-tree bulk loading algorithms.Our algorithms minimize the number of distance computations and disk accesses using FastMap and a space-filling curve,thereby significantly improving the index construction and search performance.Our second algorithm is an extension of the first,and it incorporates a partitioning clustering technique and flexible node architecture to further improve the search performance.Through the use of various synthetic and real-world datasets,the experimental results demonstrated that our algorithms improved the index construction performance by up to three orders of magnitude and the search performance by up to 20.3 times over the previous algorithm.

Research on a toolpath generation method of NC milling based on space-filling curve

Tool path generated by space-filling curve always turns frequently causing trembling to machine,reducing toollife and affecting workpiece quality. Length and generation time of tool paths are both relatively long. In order to solve these problems,a toolpath generation method of NC milling based on space-filling curve is proposed. First,T-spline surface is regarded as the modeling surface,the grid,which is based on the limited scallop-height,can be got in the parameter space,and the influence value of grid node is determined. Second,a box is defined and planned,and the tool paths are got preliminarily,which is based on minimal spanning tree; Finally,based on an improved chamfering algorithm,the whole tool paths are got. A simulation system is developed for computer simulation,and an experiment is carried out to verify the method. The results of simulation and experiment show that the method is effective and feasible,and length and time of the tool paths are reduced.

An Improved Hilbert Curve for Parallel Spatial Data Partitioning

A novel Hilbert-curve is introduced for parallel spatial data partitioning, with consideration of the huge-amount property of spatial information and the variable-length characteristic of vector data items. Based on the improved Hilbert curve, the algorithm can be designed to achieve almost-uniform spatial data partitioning among multiple disks in parallel spatial databases. Thus, the phenomenon of data imbalance can be significantly avoided and search and query efficiency can be enhanced.

Oscillatory hyper Hilbert transforms along curves

The hyper Hilbert transform Tnf（x） =∫-1^1 f（x - Γ（t））e^-i｜t｜-β｜t｜^-1-αdt along an appropriate curve Γ（t） on R^n is investigated,where β 〉 α 〉 0.An L^p boundedness theorem of T4 is obtained,which is an extension of some earlier results of n = 2 and n = 3.

Riemann-Hilbert problem for first order complex equations of mixed type with degenerate curve

This paper considers the Riemann-Hilbert problem for linear mixed（elliptichyperbolic） complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.

高效前缀约简的三维Hilbert空间填充曲线编解码算法

3维Hilbert空间填充曲线(3D HSFC)的编码和解码效率对空间查询处理、图像处理等领域的应用举足轻重。现有的3维编解码算法独立编解码每一个点,忽略了Hilbert曲线的局部保持特性。为了提高编解码效率,该文设计了高效的3D状态视图,并提出一种新的前缀约简的3D HSFC编码算法(PR-3HE)和前缀约简3D HSFC解码算法(PR-3HD),这两个算法通过公共前缀的定义和识别、公共前缀约简及多种优化技术来最小化需要编码的阶数,从而提高3D HSFC的编解码效率。理论上证明:当编码或解码一个k阶的窗体(窗体内总共含有2k×2k×2k个点)时,PR-3HE平均每个点的编码阶数不超过2,PR-3HD平均解码阶数不超过8/7。相对于传统的基于迭代的方法,编解码时间复杂度从O(k)降低到了O(1)。实验结果表明,该文算法在模拟数据集和真实数据集上的表现显著优于现有算法。

一种自适应的Hilbert编码算法及其并行化

高效的Hilbert曲线的编码算法作为Hilbert曲线应用的基础,具有重要的研究意义。现有编码算法多未考虑不同输入数据的影响,因此在编码时效率较低。为此,在融合高效位操作、快速置位检测等技术的基础上,提出一种自适应的Hilbert曲线编码算法Adapt-HE。该算法根据输入数据的不同,自适应地采用不同的编码策略,能较好地适应不同的数据分布。此外,基于OpenMP对该算法进行并行化,进一步提高其编码效率,且可达到较高的加速比。

基于Hilbert曲线的轨迹大数据分布式存储与索引方法

针对具有时空特征的轨迹大数据快速增长的趋势及对其快速查询的需求,传统的关系型数据库对海量轨迹数据的存储和特定的查询需求具有一定局限性,而非关系型数据库又难以满足海量数据的高效索引需求,轨迹数据的存储和索引效率仍亟待提高。本文设计并实现了一种基于HBase数据库的存储和检索的框架,以应对时空轨迹数据的高效管理。首先,构建了一种新颖的Rowkey结构,结合时空索引工具构建了GeoMesa-HBase底层存储模型;然后,融合了基于Hilbert曲线的编码技术构建空间索引,提高了轨迹数据的存储和检索效率;最后,为了评估所提方法的有效性,将其存储和查询性能与传统存储数据库(HBase和MySQL)和Geohash索引进行比较。试验结果表明,本文方案能够有效提升轨迹数据的存储和检索效率,这对于应对轨迹大数据管理领域面临的多项挑战具有重要现实意义。

An application of space-filling curves to improve results of turbulent aerodynamics modeling with convolutional neural networks

When carrying out calculations for turbulent flow simulation,one inevitably has to face the choice between accuracy and speed of calculations.In order to simultaneously obtain both a computationally efficient and more accurate model,a surrogate model can be built on the basis of some fast special model and knowledge of previous calculations obtained by more accurate base models from various test bases or some results of serial calculations.The objective of this work is to construct a surrogate model which allows to improve the accuracy of turbulent calculations obtained by a special model on unstructured meshes.For this purpose,we use 1D Convolutional Neural Network(CNN)of the encoder-decoder architecture and reduce the problem to a single dimension by applying space-filling curves.Such an approach would have the benefit of being applicable to solutions obtained on unstructured meshes.In this work,a non-local approach is applied where entire flow fields obtained by the special and base models are used as input and ground truth output respectively.Spalart-Allmaras(SA)model and Near-wall Domain Decomposition(NDD)method for SA are taken as the base and special models respectively.The efficiency and accuracy of the obtained surrogate model are demonstrated in a case of supersonic flow over a compression corner with different values for angleαand Reynolds number Re.We conducted an investigation into interpolation and extrapolation by Re and also into interpolation byα.

基于Hilbert扫描和小波变换的自适应图像分割

阈值的选择是图像阈值分割法的关键,针对现有阈值法中存在的没有充分地考虑图像像素之间的空间相关信息等问题,提出把Hilbert图像扫描方法和小波变换相结合,获得了连续光滑的阈值曲线,从而建立了一种局部自适应阈值法。首先通过Hilbert图像扫描的方法将2维图像信息转化为1维Hilbert序列;然后利用小波变换对其进行多分辨分析获得信号的发展趋势曲线,并将该曲线作为阈值曲线对Hilbert序列进行量化处理;最后对量化后的Hilbert序列运用Hilbert图像扫描的反过程恢复为2维图像信息,从而实现原图像的分割。该方法所建立的阈值曲线能够随像素点的环境变化而自适应调整,反映出当前区域图像灰度信息的变化趋势,从而充分地保留了图像的局部信息和原图像中相邻像素的相关性,提高了图像分割效率。实验结果表明,该方法具有分割性能好以及受噪声影响小等优点,是一种非常有效的图像分割方法。

基于状态视图的高效Hilbert编码和解码算法

Hilbert曲线是高维降到1维的重要方法,具有较好的空间聚集和空间连续性,在地理信息系统、空间数据库、信息检索等方面有广泛的应用。现有Hilbert编码或解码算法未考虑输入数据对编码或解码效率的影响,因此将不同输入数据同等对待。为此,该文通过设计高效的状态视图并结合快速置位检测算法提出高效的免计前0的Hilbert编码算法(FZF-HE)和免计前0的Hilbert解码算法(FZF-HD),可快速识别输入数据前部为0而无需迭代计算的部分,从而降低迭代查询次数及算法复杂度,提高编解码效率。实验结果表明,FZF-HE算法和FZF-HD算法在数据均匀分布时效率稍高于现有算法,而在数据偏斜分布时效率远高于现有算法。

基于Hilbert填充曲线的自适应隐写

自适应隐写用于将适量的消息比特嵌入到载体以取得感知质量和容量的最佳折衷.本文提出一种基于量化嵌入机制的自适应隐写方法,并基于该方法将秘密消息比特嵌入到由Hilbert填充曲线顺序构造的三像素组的两像素差中.由于充分利用图像本身的感知特性构造了量化嵌入使用的分割码本,所提算法在感知质量和容量上具有较好的综合性能.

图象扫描波动性度量及Hilbert扫描矩阵的快速生成

在图象扫描技术中 ,首要的问题是如何尽量减小生成数据的波动性 .为此在深入研究各种扫描技术的基础上 ,定义了一种描述扫描方式产生数据波动性的度量指标 ,基于图象存在局部连续性 ,证明了Hilbert分形曲线扫描优于其他传统扫描 ,表明其生成数据的最佳连续特性 ,并通过实验分析了图象扫描方式对DCT变换编码效果的影响 .最后 ,给出了一个构造Hilbert扫描矩阵的快速算法 ,以方便该方法的进一步研究及应用 .

Hilbert曲线扫描矩阵的生成算法及其MATLAB程序代码

H ilbert曲线是一种重要的图像处理工具,在图像处理,特别是图像扫描中广泛应用。为了正确快速的生成H ilbert曲线扫描矩阵,提出了基于矩阵运算的生成H ilbert曲线扫描矩阵的新算法,并给出了MATLAB仿真语言的程序代码,同时用数学归纳法从理论上证明了该算法的正确性。由计算机仿真可见该算法的正确性和简单易行,最后给出了一个简单的应用例子。

N维Hilbert编码的计算

针对高维Hilbert曲线的复杂性问题,给出了一种N维Hilbert码计算方法.其基本思想是面向一个称为基因的静态演化规则表,根据基因信息进行相应的坐标变换,编解码始终依照Hilbert单元的映射特征进行映射转换;在逐层编解码过程中,把不断变化的映射形态转成固定的Hilbert单元映射方式,同时采用二进制位操作进行计算,从而实现高效的N维Hilbert映射转换.

Hilbert曲线的快速生成算法设计与实现

研究了Hilbert曲线的特征和现有经典算法,依据二分技术提出了一种全新的空间填充曲线生成算法．算法按照复制 的思想将具有“形”特征的曲线问题转化为具有“数”特征的矩阵问题．因此对由线的操作就转化为对矩阵的运算,而短阵运算不 用考虑绘制曲线方向问题,也不用考虑曲线始点和终点．实验结果表明,该算法比经典的L系统算法提高了将近1倍的速度．有 意义的是,该算法为并行计算大型空间填充曲线提出了一种方案．

N维Hilbert曲线生成算法

H ilbert曲线描述了一种多维空间与1维空间一一映射的方法,在图像处理、多维数据索引等领域有着重要的地位。但因为高维H ilbert曲线的复杂性,对高维H ilbert的相关算法研究很少。提出了产生N维H ilbert曲线的一个新算法。该算法基于静态演化规则,自底向上地分析N维H ilbert曲线编码规律,实现N维H ilbert曲线的编码生成。与现有的算法相比,本文算法易于实现。实验结果表明,该算法具有更好的计算性能。

一种Hilbert变换法在非线性系统分析中的应用

Hilbert变换是信号处理领域常用工具之一,将Hilbert变换法改进并应用到信号分解和非线性系统振动分析中。振动信号的多谐波性,使得Hilbert变换法提取信号的瞬时频率和瞬时相角可以通过滤波的方法分离成快变和慢变两部分,从而提取系统的振动分量;通过迭代计算,依次获得振动信号中所有谐波分量;将非线性振动方程用瞬态幅值相关的瞬态参数表示,从而求解系统的频响关系曲线方程。通过相应的数值模拟计算,验证了改进的Hilbert变换法在非线性振动分析的有效性。

三维Hilbert曲线在图像置乱中的应用

研究三维Hilbert曲线基元在空间中的24种形态,提出一种基于基元分形走向的n阶三维Hilbert曲线生成算法,将图像像素点存入到一个空间立方体数组中,按三维Hilbert曲线遍历顺序对空间立方体中的像素点进行顺序扫描存储,从而实现图像置乱处理。实验结果表明,相比二维Hilbert曲线,三维Hilbert曲线置乱具有更强的图像置乱度和更高的图像加密安全性。