数据仓库系统中层次式Cube存储结构

区域查询是数据仓库上支持联机分析处理(on-line analytical processing,简称OLAP)的重要操作.近几年,人们提出了一些支持区域查询和数据更新的Cube存储结构.然而这些存储结构的空间复杂性和时间复杂性都很高,难以在实际中使用.为此,提出了一种层次式Cube存储结构HDC(hierarchical data cube)及其上的相关算法.HDC上区域查询的代价和数据更新代价均为O(log^dn),综合性能为O((logn)^2d)(使用C_qC_u模型)或O(K(logn)^d)(使用C_qn_q+C_un_u模型).理论分析与实验表明,HDC的区域查询代价、数据更新代价、空间代价以及综合性能都优于目前所有的Cube存储结构.     

虫孔路由Mesh上的连通分量算法及其应用

用倍增技术在带有Wormhole路由技术的n×n二维网孔机器上提出了时间复杂度为O(log²n)的连通分量和传递闭包并行算法,并在此基础上提出了一个时间复杂度为O(log³n)的最小生成树并行算法.这些都改进了Store-and-Forward路由技术下的时间复杂度下界O(n).同其他运行在非总线连接分布式存储并行计算机上的算法相比,此连通分量和传递闭包算法的时间复杂度是最优的.     

无存储器冲突的并行快速排序算法*

本文在一个EREW PRAM(exclusive read exclusive write paralled random accessmachine)上提出一个并行快速排序算法，这个算法用k个处理器可将n个项目在平均O((n/k+logn)logn)时间内排序．所以平均来说算法的时间和处理器数量的乘积对任何k≤n/logn是 O(nlogn)．     

三维空间中的最短路问题

在包含一组相互分离凸多面体的三维空间中为任意两点寻找最短路的问题是NP问题.当凸多面体的个数k任意时,它为指数时间复杂度;而当k=1时,为O(n²)（n为凸多面体的顶点数）.文章主要研究了k=2情形下的最短路问题,提出一个在O(n²)时间内解决该问题的算法.所得结果大大优于此情形下迄今为止最好的结果——O(n^{3相似文献}   

一类可分离SAT问题的O(1.890n)精确算法

布尔可满足性问题（SAT）是指对于给定的布尔公式,是否存在一个可满足的真值指派.这是第1个被证明的NP完全问题,一般认为不存在多项式时间算法,除非P=NP.学者们大都研究了子句长度不超过k的SAT问题（k-SAT）,从全局搜索到局部搜索,给出了大量的相对有效算法,包括随机算法和确定算法.目前,最好算法的时间复杂度不超过O（（2-2/k）ⁿ）,当k=3时,最好算法时间复杂度为O（1.308ⁿ）.而对于更一般的与子句长度k无关的SAT问题,很少有文献涉及.引入了一类可分离SAT问题,即3-正则可分离可满足性问题（3-RSSAT）,证明了3-RSSAT是NP完全问题,给出了一般SAT问题3-正则可分离性的O（1.890ⁿ）判定算法.然后,利用矩阵相乘算法的研究成果,给出了3-RSSAT问题的O（1.890ⁿ）精确算法,该算法与子句长度无关.     

PRAM和LARPBS模型上有向序列翻转距离并行算法

分别在两种重要并行计算模型中给出计算有向基因组排列的反转距离新的并行算法.基于Hannenhalli和Pevzner理论,分3个主要部分设计并行算法:构建断点图、计算断点图中圈数、计算断点图中障碍的数目.在CREW-PRAM模型上,算法使用O(n²)处理器,时间复杂度为O(log²n);在基于流水光总线的可重构线性阵列系统(linear array with a reconfigurable pipelined bus system, LARPBS)模型上,算法使用O(n³)处理器,计算时间复杂度为O(logn).     

确定任意多边形凸凹顶点的算法

本文提出一种确定任意多边形凸凹顶点的算法．该算法的时间复杂性为O(n²logn)次乘法和O(n²)次比较．     

求解大规模谱聚类的近似加权核k-means算法

谱聚类将聚类问题转化成图划分问题,是一种基于代数图论的聚类方法.在求解图划分目标函数时,一般利用Rayleigh熵的性质,通过计算Laplacian矩阵的特征向量将原始数据点映射到一个低维的特征空间中,再进行聚类.然而在谱聚类过程中,存储相似矩阵的空间复杂度是O(n²),对Laplacian矩阵特征分解的时间复杂度一般为O(n³),这样的复杂度在处理大规模数据时是无法接受的.理论证明,Normalized Cut图聚类与加权核k-means都等价于矩阵迹的最大化问题.因此,可以用加权核k-means算法来优化Normalized Cut的目标函数,这就避免了对Laplacian矩阵特征分解.不过,加权核k-means算法需要计算核矩阵,其空间复杂度依然是O(n²).为了应对这一挑战,提出近似加权核k-means算法,仅使用核矩阵的一部分来求解大数据的谱聚类问题.理论分析和实验对比表明,近似加权核k-means的聚类表现与加权核k-means算法是相似的,但是极大地减小了时间和空间复杂性.     

一种高效频繁子图挖掘算法

由于在频繁项集和频繁序列上取得的成功,数据挖掘技术正在着手解决结构化模式挖掘问题--频繁子图挖掘.诸如化学、生物学、计算机网络和WWW等应用技术都需要挖掘此类模式.提出了一种频繁子图挖掘的新算法.该算法通过对频繁子树的扩展,避免了图挖掘过程中高代价的计算过程.目前最好的频繁子图挖掘算法的时间复杂性是O(n³·2ⁿ),其中,n是图集中的频繁边数.提出算法的时间复杂性是O〔2ⁿ·n^2.5／logn〕,性能提高了O(√n·logn)倍.实验结果也证实了这一理论分析.     

模糊聚类计算的最佳算法

给出模糊关系传递闭包在对应模糊图上的几何意义,并提出一个基于图连通分支计算的模糊聚类最佳算法.对任给的n个样本,新算法最坏情况下的时间复杂性函数T(n)满足O(n)≤T(n)≤O(n²).与经典的基于模糊传递闭包计算的模糊聚类算法的O(n³logn)计算时间相比,新算法至少降低了O(n相似文献   

Improved update/query algorithms for the interval valuation problem

Let I be the set of intervals with endpoints in the integers 1, 2, …, n. Associated with each element in I is a value from a commutative semigroup S. Two operations are to be implemented: update of the value associated with an interval, and query of the sum of the values associated with the intervals which include an integer. If the values are from a commutative group (i.e., inverses exist), then there is a data structure which enables both update and query algorithms of time complexity O(log n). For the semigroup problem, the use of range trees enables both uptade and query algorithms of time complexity O(log² n). Data structures are presented for the semigroup problem with (update, query) algorithms of complexities (log n, log² n) and (log n log log n, log n).     

Fast dynamic intersection searching in a set of isothetic line segments

We reconsider the (isothetic) line segment intersection searching problem: Given a set S of n horizontal and vertical line segments and a query segment q, find all t segments in S intersecting q. We describe the first dynamic solution for this problem which achieves O(log n + t) query time. This, however, has to be paid by O(n log² n) space requirements and O(log³ n) update time. If segments are defined over a grid of size N × N (the semidynamic case), then the problem can be solved in O(logN + t) query time, O(n log² N) space and O(log² N) update time. The solution is based on the use of segment tree and range tree and the halfobject technique.     

Fully dynamic maintenance of k-connectivity in parallel

Given a graph G=(V, E) with n vertices and m edges, the k-connectivity of G denotes either the k-edge connectivity or the k-vertex connectivity of G. In this paper, we deal with the fully dynamic maintenance of k-connectivity of G in the parallel setting for k=2, 3. We study the problem of maintaining k-edge/vertex connected components of a graph undergoing repeatedly dynamic updates, such as edge insertions and deletions, and answering the query of whether two vertices are included in the same k-edge/vertex connected component. Our major results are the following: (1) An NC algorithm for the 2-edge connectivity problem is proposed, which runs in O(log n log(m/n)) time using O(n^3/4) processors per update and query. (2) It is shown that the biconnectivity problem can be solved in O(log^{2 n} ) time using O(nα(2n, n)/logn) processors per update and O(1) time with a single processor per query or in O(log n log_n/^m) time using O(nα(2n, n)/log n) processors per update and O(logn) time using O(nα(2n, n)/logn) processors per query, where α(.,.) is the inverse of Ackermann's function. (3) An NC algorithm for the triconnectivity problem is also derived, which takes O(log n log_n/^m+logn log log n/α(3n, n)) time using O(nα(3n, n)/log n) processors per update and O(1) time with a single processor per query. (4) An NC algorithm for the 3-edge connectivity problem is obtained, which has the same time and processor complexities as the algorithm for the triconnectivity problem. To the best of our knowledge, the proposed algorithms are the first NC algorithms for the problems using O(n) processors in contrast to Ω(m) processors for solving them from scratch. In particular, the proposed NC algorithm for the 2-edge connectivity problem uses only O(n^3/4) processors. All the proposed algorithms run on a CRCW PRAM     

Parallel Algorithms for Image Template Matching on Hypercube SIMD Computers

This correspondence presents several parallel algorithms for image template matching on an SIMD array processor with a hypercube interconnection network. For an N by N image and an M by M window, the time complexity is reduced from O(N2M2) for the serial algorithm to O(M2/K2 + M * log2 N/K + log2 N * log2 K) for the N2K2-PE system (1 ? K ? M), or to O(N2M2/L2) for the L2-PE system (L ? N). With efficient use of the inter-PE communication network, each PE requires only a small local memory, many unnecessary data transmissions are eliminated, and the time complexity is greatly reduced.     

受限网络模糊对象最近邻查询

针对网络空间中有范围约束、不确定对象的最近邻查询问题,提出范围受限的网络空间模糊对象最近邻查询概念,并根据查询顺序的不同,给出NN-R查询算法和R-NN查询算法。两种算法均采用网络位置信息与连接信息分别存储的方式,使用聚类文件进行组织,减少I/O操作。NN-R算法在近邻查询过程中利用查询对象与受限范围的α-距离作为约束,缩小搜索范围。R-NN算法将受限范围内查询对象的欧氏近邻作为候选对象,利用欧氏距离的下界性与易求性降低时间复杂度。两种算法时间复杂度分别为O((log_(m1)|E|+(|V~*|m3+1)log_(m2)|V|+|E|+|V|log|V|+n(lgn+1))和O(log_(m4)n+(k+1)log_(m1)|E|+|E|+|V|log|V|)。实验结果表明,在各自适用条件下,两种算法均有较好的性能。     

Improved algorithms for searching restriction maps.

We present algorithms for searching a DNA restriction enzyme map for a region that best matches a shorter 'probe' map. Our algorithms utilize a new model of map alignments, and extensive experiments prove our model superior to earlier approaches for certain applications. Let M be the number of map sites and P be the number of probe sites. Our first algorithm, which optimizes only over a restricted class of alignments, requires O(MP log P) worst-case time and O(M + P) space. Our second algorithm, which optimizes over all alignments, runs in O(MP3) time and O(M + P2) space, under reasonable assumptions about the distribution of restriction enzyme cleavage sites. Combining the algorithms gives a map-searching method that optimizes over all alignments in O(MP log P) time in practice. The algorithms' effectiveness is illustrated by searches involving a genomic restriction map of Escherichia coli.     

Fast Range Searching with Delaunay Triangulations

This paper studies the idea of answering range searching queries using simple data structures. The only data structure we need is the Delaunay Triangulation of the input points. The idea is to first locate a vertex of the (arbitrary) query polygon and walk along the boundary of the polygon in the Delaunay Triangulation and report all the points enclosed by the query polygon. For a set of uniformly distributed random points in 2-D and a query polygon the expected query time of this algorithm is O(n ^1/3 + Q + E K + L _r n ^1/2), where Q is the size of the query polygon , {\bf E}K = O(n\bcdot area is the expected number of output points, L _r is a parameter related to the shape of the query polygon and n, and L _r is always bounded by the sum of the edge lengths of . Theoretically, when L _r = O(1/n^1/6) the expected query time is O(n^1/3 + Q + E K), which improves the best known average query time for general range searching. Besides the theoretical meaning, the good property of this algorithm is that once the Delaunay Triangulation is given, no additional preprocessing is needed. In order to obtain empirical results, we design a new algorithm for generating random simple polygons within a given domain. Our empirical results show that the constant coefficient of the algorithm is small, at least for the special (practical) cases when the query polygon is either a triangle (simplex range searching) or an axis-parallel box (orthogonal range searching) and for the general case when the query polygons are generated by our new polygon-generating algorithms and their sizes are relatively small.     

基于RDF图结构切分的高效子图匹配方法

针对在SPARQL查询处理中,随着查询图结构逐渐复杂而导致基于图的查询效率愈发低下的问题,通过分析几种资源描述框架（RDF）图的基本结构,提出了一种基于查询图结构切分的子图匹配方法——RSM。首先,将查询图切分为若干结构简单的查询子图,并通过相邻谓词结构索引来定义查询图节点的搜索空间;然后,通过相邻子图结构来缩小搜索空间范围,在数据图中根据搜索空间中的搜索范围找到符合的子图结构;最后,将得到的子图进行连接并作为查询结果输出。将RSM与RDF-3X、R3F、GraSS等主流查询方法作比较,对比了各方法在不同数据集上对于复杂程度不同的查询图的查询响应时间。实验结果充分表明,与其他3种方法相比,在处理结构复杂的查询图时,RSM的查询响应时间更短,具有更高的查询效率。     

基于量子计算机的数据库搜索

Grover提出的量子搜索算法,可以用O(N1/2)的时间复杂度完成对规模为N的非结构化数据集的搜索,这在经典计算机上需要O(N)的复杂度。其中量子黑盒(又称为Oracle)依赖于具体问题,根据数据库搜索的要求,设计了量子黑盒的内部结构和相应的量子线路,给出了适合于数据库搜索的量子算法。     

关于汉字的两个分组查找算法

处理汉字的以比较为基础的二分查找算法, 其复杂性为O(NlogN)。本文结合概率论知识, 提出汉字的随机分组查找算法和分组散列查找算法, 给出算法描述, 并证明其算法复杂性为O(N), 从而优于二分查找算法。最后给出实验结果。