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.     

网络流量的有效测量方法分析

把网络流量的有效测量问题抽象为求给定图G=(V,E)的最小弱顶点覆盖集的问题.给出了一个求最小弱顶点覆盖集的近似算法,并证明了该算法具有比界2(lnd+1),其中d是图G中顶点的最大度.指出了该算法的时间复杂性为O(|V|²).     

k-Median近似计算复杂度与局部搜索近似算法分析

k-Median问题的近似算法研究一直是计算机科学工作者关注的焦点,现有研究结果大多是关于欧式空间和Metric空间的,一般距离空间k-Median的结果多年来一直未见.考虑一般距离空间k-Median问题,设d_max/d_min表示k-Median实例中与客户点邻接的最长边长比最短边长的最大者.首先证明d_max/d_min≤ω+ε的k-Median问题不存在近似度小于1+ω-1/e的多项式时间近似算法,除非,由此推出Metric k-Median问题不可近似到1+2/e,除非NP(∈)DTME(N^{O(log logn)}).然后给出k-Median问题的一个局部搜索算法,分析表明,若有d_max/d_min≤ω,则算法的近似度为1+ω-1/2.该结果亦适用于Metric k-Median,ω≤5时,局部搜索算法求解Metric k-Median的近似度为3,好于现有结果3+2/P.通过计算机实验,进一步研究了k-Median局部搜索求解算法的实际计算效果和该算法的改进方法.     

光RP(k)网络上Hypercube通信模式的波长指派算法

波长指派是光网络设计的基本问题,设计波长指派算法是洞察光网络通信能力的基本方法.基于光RP(k)网络,讨论了其波长指派问题. 含有N=2ⁿ个节点的Hypercube通信模式,构造了节点间的一种排列次序Xn,并设计了RP(k)网络上的波长指派算法.在构造该算法的过程中,得到了在环网络上实现n维Hypercube通信模式的波长指派算法.这两个算法具有较高的嵌入效率.在RP(k)网络上,实现Hypercube通信模式需要max{2,「5(2^n-5/3」}个波长.而在环网络上,实现该通信模式需要复用(N/3+N/12(个波长,比已有算法需要复用「N/3+N/4」个波长有较大的改进.这两个算法对于光网络的设计具有较大的指导价值.     

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.     

背包问题的最优并行算法

利用分治策略,提出一种基于SIMD共享存储计算机模型的并行背包问题求解算法.算法允许使用O(2^n/4)^1-ε个并行处理机单元,0≤ε≤1,O(2^n/2)个存储单元,在O(2^n/4(2^n/4)^ε)时间内求解n维背包问题,算法的成本为O(2^n/2).将提出的算法与已有文献结论进行对比表明,该算法改进了已有文献的相应结果,是求解背包问题的成本最优并行算法.同时还指出了相关文献主要结论的错误.     

RNA二级结构预测中动态规划的优化和有效并行

基于最小自由能模型的方法是计算生物学中RNA二级结构预测的主要方法,而计算最小自由能的动态规划算法需要O(n⁴)的时间,其中n是RNA序列的长度.目前有两种降低时间复杂度的策略:限制二级结构中内部环的大小不超过k,得到O(n²×k²)算法;Lyngso方法根据环的能量规则,不限制环的大小,在O(n3)的时间内获得近似最优解.通过使用额外的O(n)的空间,计算内部环中的冗余计算大为减少,从而在同样不限制环大小的情况下,在O(n³)的时间内能够获得最优解.然而,优化后的算法仍然非常耗时,通过有效的负载平衡方法,在机群系统上实现并行程序.实验结果表明,并行程序获得了很好的加速比.     

加权3-Set Packing 的改进算法

Packing 问题构成了一类重要的NP 难问题.对于加权3-Set Packing 问题,把问题转化成加权3-Set Packing Augmentation 问题进行求解,即主要讨论如何从一个已知的最大加权k-packing 求得一个权值最大的(k+1)-packing. 通过对问题结构的分析,结合Color-Coding 技术,首先给出了一种时间复杂度为O^*(10.6^3k)的参数算法,极大地改进了目前文献中的最好结果O^*(12.8^3k).通过对(k+1)-packing 结构的进一步分析,利用集合划分技术将上述结果降到O^*(7.56^3k).     

不同通信模型下的全光树环网波长分配算法

研究了波分复用全光树环网在不同通信模型下的波长分配算法及其最坏性能分析.对于静态模型,证明了5L/2是树环网所需波长数的紧界.对于动态模型,提出了一种近似比为∑_i=1^hmax_r∈Ri[log|V(r)|]+h的波长分配算法,其中h为树环网的基树的层数,R_i为树环网中处于第i层的环的集合,|V(r)|为环r上的节点数.对于增量模型,提出了一种近似度为O[log₂(t+1)]的波长分配算法,其中t为树环网中的环数.     

近乎最佳的Manhattan型Steiner树近似算法

求解最佳的Manhattan型Steiner树问题(minimum rectilinear Steiner tree,简记为MRST问题)是在VLSI布线、网络通信中所遇到的组合优化问题,同时也是一个NP-难解问题.该文给出对该问题的O(n²)时间复杂性的近似算法.该算法在最坏情况下的近似比严格小于3/2.计算机实验结果表明,所求得的支撑树的平均费用与最佳算法的平均费用仅相差0.8%.该算法稍加修改,可应用到三维或多维的Manhattan空间对Steiner问题求解,且易于在并行与分布式环境下编程实现     

H-Torus拓扑结构等分带宽的计算

针对H-Torus拓扑结构,给出两种确定该拓扑结构等分带宽上、下界的方法.这些方法同样适用于2D Torus拓扑结构.还提出了H-Torus结构等分带宽的精确求解方案,但是该算法的复杂度过大,只适用于网络规模较小的情况.实验表明,H-Torus拓扑结构的等分带宽大于同等规模的2D Torus结构,更有利于提高路由器的吞吐率.与现有的研究结果相比,所提出的等分带宽上、下界在精度上有了较大的提高,这为可扩展路由器的性能评估提供了有力的支持.     

New spectral lower bounds on the bisection width of graphs

The communication overhead is a major bottleneck for the execution of a process graph on a parallel computer system. In the case of two processors, the minimization of the communication can be modeled using the graph bisection problem. The spectral lower bound of λ₂|V|/4 for the bisection width of a graph is widely known. The bisection width is equal to λ₂|V|/4 iff all vertices are incident to λ₂/2 cut edges in every optimal bisection.

We present a new method of obtaining tighter lower bounds on the bisection width. This method makes use of the level structure defined by the bisection. We define some global expansion properties and we show that the spectral lower bound increases with this global expansion. Under certain conditions we obtain a lower bound depending on λ₂^β|V| with . We also present examples of graphs for which our new bounds are tight up to a constant factor. As a by-product, we derive new lower bounds for the bisection widths of 3- and 4-regular Ramanujan graphs.     

A gradient method for computing the optimal H/sub infinity / norm

A fast algorithm for computing the optimal H/sub infinity / norm is presented. The algorithm is based on certain explicit computations of gradients. Examples are given to show that the gradient method is much faster than the bisection method. The gradient method can be used without the upper and lower bound computations. This could be a substantial additional saving because computing these bounds requires the computation of the H/sub infinity / norm.<>     

Asymptotic Dynamic Time Warping calculation with utilizing value repetition

Dynamic Time Warping (DTW) is a popular method for measuring the similarity of time series. It is widely used in various domains. A major drawback of DTW is that it has a high computational complexity. To address this problem, pruning techniques to calculate the exact DTW distance, as well as DTW approximation methods, have become important approaches. In this paper, we introduce Blocked Dynamic Time Warping (BDTW), a new similarity measure which works on run-length encoded time series representation. BDTW utilizes any repetitive values (zero and nonzero) in time series to reduce DTW computation time. BDTW closely approximates DTW distance, and it is significantly faster than traditional DTW for time series with high levels of value repetition. Moreover, BDTW can be combined with time series representation methods which provide constant segments, to serve as a close approximation method even for the time series without value repetition. Constrained BDTW, BDTW upper bound and BDTW lower bound are discussed as variations of BDTW. BDTW upper bound and BDTW lower bound are presented as a new DTW upper bound and lower bound which can be efficiently applied on time series with high levels of value repetition for pruning unhopeful alignments and matches in the exact DTW calculation. We show the effectiveness of BDTW and its variations on different applications using the following datasets: Almanac of Minutely Power, Refit Smart Homes, as well as the 85 datasets from the University of California, Riverside time series classification archive (UCR archive).     

图的Steiner最小树问题的降阶回溯算法

图的Steiner最小树问题是经典的组合优化问题,是一个NP难题,在不同的领域有着广泛的应用。研究该问题的部分数学性质,在此基础上给出了该问题的初步降阶方法和下界子方法,形成一个新的回溯算法。该算法具有较低的时间复杂度,还给出了应用实例及其分析。     

Research on Next-Generation Scalable Routers Implemented with H-Torus Topology

The exponential growth of user traffic has been driving routers to run at higher capacity. In a traditional router, the centralized switching fabric is becoming the bottleneck for its limited number of ports and complicated scheduling algorithms. Direct networks, such as 3-D Torus topology, have been successfully applied to the design of scalable routers. They show good scalability and fault tolerance. Unfortunately, its scalability is limited in practice. In this paper, we introduce another type of direct network, called H-Torus. This network shows excellent topological properties. On its basis, the designs of line card and routing algorithms are introduced. Extensive simulations show that the routing algorithm is very important in such a system and results in low latency with high throughput.     

Fast conflict detection using probability flow

Probabilistic conflict detection has recently attracted much attention from researchers due to its importance in safe automated transport systems; however, current methods struggle to accurately calculate in real-time the probability of conflict for complex vehicle maneuvers in cluttered environments. We present a formulation for the general probabilistic conflict detection problem using the flow rate of conflict probability at the boundary of a conflict zone. For Gaussian distributed vehicle states, we then derive a tight upper bound for the probability of conflict over a time period, which can be calculated in real-time using adaptive numerical integration techniques. We present two examples to illustrate the performance of this method: the first example shows that this method is very efficient for simple environments and the second example shows that this method can calculate the conflict probability upper bound in real-time even for complex vehicle maneuvers in cluttered environments.     

正形置换的枚举与计数

正形置换在密码算法的设计中占有很重要的地位．研究正形置换的特性、枚举、计数对于密码设计和密码分析均具有重要的意义．正形置换的理论研究已成为国内外密码学编码理论的热点问题．对正形置换的计数和枚举问题进行讨论，利用和阵给出了正形置换的一个枚举方法，利用该方法可以列出所有的”阶正形置换．国内外相关文献中还未见到正形置换的枚举方法．由该枚举法得出了n阶正形置换个数Nn的上界和下界，这个结果比迄今为止给出的结果都要好，是目前给出的最优上下界．     

评估网络整体连通概率的算法

提出了一种评估网络整体连通概率的新方法.该方法提出了如何化简网络状态空间,并将状态空间进行多级分解,以缩减状态向量的规模.对分解所得的每一个网络状态向量,提出一种构造子网的方法来判断此向量的是否能保持原网络的连通性,通过迭代运算用网络整体连通概率的上下界来估计其真实值.与传统算法相比,该方法具有计算速度快、收敛性好、通用性较强,适合大规模网络近似计算的特点.     

COMPUTATION OF BEST BOUNDS OF PROBABILITIES FROM UNCERTAIN DATA

An uncertainty reasoning method is presented in this article. The method can be used to compute from a given set of conditional probabilities the best lower bounds and the best upper bounds of those conditional probabilities that are not explicitly provided. The computation of the best upper(lower) bound of such a conditional probability relies on solution of a linear programming problem. Some reduction techniques are proposed in this article to improve the efficiency of our uncertainty reasoning method. As illustrated in Section 4.3, for many uncertainty reasoning problems in medical diagnosis, by using our reduction techniques, the best range of a conditional probability, which is specified by a lower bound and an upper bound, can be computed in polynomial time in terms of the number of basic events involved in the reasoning.