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dmax/dmin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dmax/dmin≤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(NOlog logn)).然后给出k-Median问题的一个局部搜索算法,分析表明,若有dmax/dmin≤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.     

Goguen命题逻辑系统公理化扩张的Γ-k真度理论及性质

本文首先对n值Goguen命题逻辑进行公理化扩张,Goguen_~,△,记为Π_~,△.利用公式的诱导函数给出公式在k（k任取~或△）连接词下相对于局部有限理论Γ的Γ-k真度的定义;讨论了Π_~,△中Γ-k真度的MP规则、HS规则等相关性质;最后,在Π_~,△中定义了两公式间的Γ-k相似度与Γ-k伪距离,得到了公式在连接词下相对于局部有限理论Γ的Γ-k相似度与Γ-k伪距离所具有的一些良好性质.     

P2-Packing问题参数算法的改进

P₂-Packing问题是一个典型的NP难问题.目前这个问题的最好结果是时间复杂度为O^*(2^5.301k)的参数算法,其核的大小为15k.通过对P₂-packing问题的结构作进一步分析,提出了改进的核心化算法,得到大小为7k的核,并在此基础上提出了一种时间复杂度为O^*(2^4.142k)的参数算法,大幅度改进了目前文献中的最好结果.     

取定s的严格d-正则随机(3,2s)-SAT问题的可满足临界

3-CNF公式的随机难解实例生成对于揭示3-SAT问题的难解实质和设计满足性测试的有效算法有着重要意义.对于整数k>2和s>0,如果在一个k-CNF公式中每个变量正负出现次数均为s,则称该公式是严格正则（k,2s）-CNF公式.受严格正则（k,2s）-CNF公式的结构特征启发,提出每个变量正负出现次数之差的绝对值均为d的严格d-正则（k,2s）-CNF公式,并使用新提出的SDRRK2S模型生成严格d-正则随机（k,2s）-CNF公式.取定整数5<s<11,模拟实验显示,严格d-正则随机（3,2s）-SAT问题存在SAT-UNSAT相变现象和HARD-EASY相变现象.因此,立足于3-CNF公式的随机难解实例生成,研究了严格d-正则随机（3,2s）-SAT问题在s取定时的可满足临界.通过构造一个特殊随机实验和使用一阶矩方法,得到了严格d-正则随机（3,2s）-SAT问题在s取定时可满足临界值的一个下界.模拟实验结果验证了理论证明所得下界的正确性.     

一种基于彩色编码技术的基序发现算法

从DNA序列中发现基序是生物计算中的一个重要问题,序列条数K=20包含基序用例的序列条数k=16的(l,d)-(K-k)问题(记作(l,d)-(20-16)问题)是目前生物学家十分关注的基序发现问题.针对该问题提出了一种基于彩色编码技术的SDA(sample-driven algorithm)搜索算法--彩色编码基序搜索算法(color coding motif finding algorithm,简称CCMF算法).它利用彩色编码技术将该问题转化为(l,d)-(16-16)问题,再采用分治算法和分支定界法来求解.在解决将(l,d)-(20-16)问题转化为(l,d)-(16-16)问题时,CCMF算法利用彩色编码技术将4 845个组合降低到403个着色,这将极大地提高算法的整体运行效率.使用模拟数据和生物数据进行测试的结果表明,CCMF算法能够快速发现所有(l,d)-(20-16)问题的基序模型和基序用例,具有优于其他算法的综合性能评价,能够用于真实的基序发现问题.同时,通过修改着色方案,CCMF算法可以用于求解一般的(l,d)-(K-k)问题,其中,k＜K.     

一般设施定位问题计算复杂度和近似算法研究

设施定位问题即UFL问题是NP-hard的组合优化问题,是聚类问题领域的热点问题之一,在数据挖掘和分类识别方面有着重要应用.多年来其近似算法研究一直是计算机科学工作者关注的焦点,然而现有研究结果大多关于Metric空间,一般距离空间中该问题结果始终未见.针对最大连接费用至多是最小连接费用ω＞1倍的一般距离空间中设施定位问题,简称一般设施定位问题,借助集合覆盖问题,利用问题归约方法证明其不存在近似性能比小于1.243 0.316ln(ω-1)的多项式时间近似算法,除非NPDTIME(nO(log log n));设计了一般设施定位问题的局部搜索算法,证明算法近似性能比是(1 ω)/α,ω＞1,1≤α≤2.仿真实验表明,一般设施定位问题局部搜索算法的求解质量极高;通过实验进一步研究了该算法并给出了改进方法.     

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.     

独立多处理机任务静态调度问题的近似算法

研究独立多处理机任务静态调度问题P_m|fix|C_max,即在m个处理机系统中调度n个多处理机任务,每个任务指派到所需一组处理机上不可剥夺地执行.该问题应用广泛但早已证明为NP难问题,而且也不存在常数近似算法.分析了问题P_m|fix|C_max和其中所有任务都是单位处理机时间的特殊情形P_m|fix,p=1|C_max的调度,并利用实例划分(split scheduling,简称SS)、首次满足优先(first fit,简称FF)和最大宽度优先(large wide first,简称LWF)等方法,构造了问题P_m|fix,p=1|C_max的√2m +1近似算法和问题P_m|fix|C_max的2√m 近似算法,优于目前已有文献的最好结果.     

真实信息发布在谣言传播中的作用研究

在基本谣言传播模型的基础上引入真实信息因素,构建了SIH谣言传播模型,并借助Monte Carlo模拟对模型进行了仿真。模型分别从真实信息发布时刻,真实信息发布者的数量、度和公信力四点研究了真实信息发布如何影响谣言的传播过程。Barabasi-Albert网络上的仿真结果表明,谣言爆发初期是谣言治理的最佳时期,真实信息的发布对谣言的传播起到扼制作用。另外,谣言传播者比例所能达到的峰值S_max与真实信息发布者所占比例η之间近似服从幂律分布S_max∝η^－μ₁;该峰值与真实信息发布者公信力提升的倍数ω之间也近似服从幂律分布S_max∝ω^－μ₂,其中指数μ₁和μ₂的大小均受到真实信息发布时间T的影响。     

有中断时间代价的一致并行机抢先调度问题

提出了一种具有中断时间代价的抢先调度问题(P|ptmn(δ)|C_max):在抢先调度中,一个任务发生一次中断,其总的执行时间会增加一个δ.该问题在工程任务分配、分布式计算和网络通信等实际问题中有着广泛的应用背景.证明了这是一个NP-hard问题,给出了一个时间复杂度为O(nlogn+m)的脱线近似算法LPT-Wrap,其近似比小于等于1.40825,并分析了P|ptmn(δ)|C_max的在线特性,给出一个线性时间复杂度的在线近似算法,其竞争比为2.     

Approximated approximations for SAO

We propose to replace a number of popular approximations by their diagonal quadratic Taylor series expansions. The resulting separable quadratic approximations are easily convexified, and are well suited for use in dual sequential approximate optimization (SAO) algorithms. Global convergence of the resulting SAO algorithms may be enforced in a natural way using conservatism. The approximated approximation approach is explicitly illustrated for (i) reciprocal and exponential intervening variables, (ii) the intervening variables used in the method of moving asymptotes (MMA), (iii) the intervening variables used in CONLIN, and (iv) the TANA-3 approximations. The use of intermediate responses for use in, for example, truss and frame-like structures, is also discussed. Key advantages of replacing nonlinear approximations by their diagonal quadratic approximations are that these approximated approximations can all be used simultaneously in a single dual statement; the dual does not depend on the form of the original approximations. In addition, in a dual setting, the resulting subproblems yield simple analytical relationships between the primal and dual variables, which is often not the case with the original nonlinear approximations. An important example hereof is the exponential approximation. Although the diagonal quadratic approximations may differ notably from their original counterparts, they typically are quite similar in a sufficiently small search subregion, which relates to the move limits commonly used in SAO anyway.     

近似Log-MAP turbo译码器研究

该文研究近似Log-M AP算法在turbo译码器中的应用。文章对基于近似算法的W CDM A turbo译码器在AW GN信道和平坦慢衰落Rayleigh信道上的纠错性能进行了仿真。仿真结果表明,二阶近似Log-M AP turbo译码器与M A P turbo译码器性能等价,优于SO VA turbo译码器0.7-0.9dB。     

Approximated Distributions of Sampling Inequality Indices

Often, in finite samples, the true level of the confidence intervals for natural estimators of inequality indices belonging to the Gini family differs greatly from their nominal level, which is based on the asymptotic confidence limits. This paper shows how the Gram-Charlier series can be used to obtain improved finite-sample confidence intervals. Our work focuses on the implementation in Mathematica 3.0 of computational procedures to compute the Gram-Charlier distribution for the following sampling inequality indices: R by Gini, P by Piesch and M by Mehran for the Dagum (Type I) distribution. The results of a Monte Carlo experiment confirm that, for the cases investigated, the Gram-Charlier distribution largely eliminates the problem of incorrect finite-sample level.     

Approximated consistency for the automatic recording constraint

We introduce the automatic recording constraint (ARC) that can be used to model and solve scheduling problems where tasks may not overlap in time and the tasks linearly exhaust some resource. Since achieving generalized arc-consistency for the ARC is NP-hard, we develop a filtering algorithm that achieves approximated consistency only. Numerical results show the benefits of the new constraint on three out of four different types of benchmark sets for the automatic recording problem. On these instances, run-times can be achieved that are orders of magnitude better than those of the best previous constraint programming approach.     

稀疏近似最近特征空间嵌入标签传播

针对现有的基于图的半监督学习（graph-based semi-supervised learning,简称GSSL）方法存在模型参数敏感和数据空间判别信息不充分等问题,受最近特征空间嵌入和数据稀疏表示思想的启发,提出一种稀疏近似最近特征空间嵌入标签传播算法SANFSP（sparse approximated nearest feature space embedding label propagation）.SANFSP首先利用特征空间嵌入投影点来稀疏表示原始数据;然后,度量原始数据和稀疏近似最近特征空间嵌入投影间的相似性;进而提出稀疏近似最近特征空间嵌入正则化项;最后,基于传统GSSL 方法的标签传播算法,实现数据标签的平滑传播.同时,还将SANFSP 算法简单拓展到out-of-sample 学习.SANFSP 算法在人造和实际数据集（如人脸识别、可视物件识别以及手写数字分类等）上取得了有效的实验结果.     

Approximated parameterized verification of infinite-state processes with global conditions

We present a simple and effective approximated backward reachability procedure for parameterized systems with existentially and universally quantified global conditions. The individual processes operate on unbounded local variables ranging over the natural numbers. In addition, processes may communicate via broadcast, rendez-vous and shared variables. The procedure operates on an over-approximation of the transition system induced by the parameterized system. We verify mutual exclusion for complex protocols such as atomic, non-atomic and distributed versions of Lamport’s bakery algorithm.     

Approximated set-valued mapping approach for handling multiobjective bilevel problems

A significant amount of research has been done on bilevel optimization problems both in the realm of classical and evolutionary optimization. However, the multiobjective extensions of bilevel programming have received relatively little attention from researchers in both the domains. The existing algorithms are mostly brute-force nested strategies, and therefore computationally demanding. In this paper, we develop insights into multiobjective bilevel optimization through theoretical progress made in the direction of parametric multiobjective programming. We introduce an approximated set-valued mapping procedure that would be helpful in the development of efficient evolutionary approaches for solving these problems. The utility of the procedure has been emphasized by incorporating it in a hierarchical evolutionary framework and assessing the improvements. Test problems with varying levels of complexity have been used in the experiments.     

Efficient Speaker Recognition Using Approximated Cross Entropy (ACE)

Techniques for efficient speaker recognition are presented. These techniques are based on approximating Gaussian mixture modeling (GMM) likelihood scoring using approximated cross entropy (ACE). Gaussian mixture modeling is used for representing both training and test sessions and is shown to perform speaker recognition and retrieval extremely efficiently without any notable degradation in accuracy compared to classic GMM-based recognition. In addition, a GMM compression algorithm is presented. This algorithm decreases considerably the storage needed for speaker retrieval.     

保持特征的平面形状近似骨架的抽取算法

针对多边形骨架抽取中轮廓噪声严重影响骨架的问题,提出一种保持特征的多边形近似骨架的抽取算法.通过分水岭算法检测平面多边形的特征突起点,在分支末端点引导骨架的抽取,从而避免多边形轮廓噪声对骨架的影响,得到有效的形状简洁的近似骨架.另外,该方法还适用于半自动的骨架抽取,即允许用户手动指定骨架末端点,使计算所得的骨架具有更高的实用性.实验结果表明,文中方法简单易行,能应用于计算机动画和形状检索等领域.