基于贝叶斯征兆解释度的链路故障定位算法

针对故障和征兆关系不确定的网络中故障定位算法检测率低和误检率高的缺陷,提出了一种基于贝叶斯征兆解释度的链路故障定位算法。该算法以概率加权的二分图作为故障传播模型,通过处理贝叶斯后验概率信息,定义一种新的参数贝叶斯征兆解释度,并基于该参数对可能链路故障进行判断,得出最优故障假设集合,实现链路故障定位。理论分析和仿真实验表明,该算法具有较低的计算复杂度,且在小规模不确定网络中具有较高的故障检测率和较低的故障误检率。     

基于故障传播模型与监督学习的电力通信网络故障定位

针对电力通信网络中的故障定位问题,分析了一种网络设备或链路故障引发的大范围连通片故障告警情形,提出一种基于故障传播模型和监督分类学习方法的故障定位算法。首先使用改进的故障传播模型求得初步定位结果,用最少的故障数目解释当前告警;然后通过故障源-故障告警向量分解将故障定位问题转化为监督分类问题,定位告警区域内部故障;最后加入猜测的故障设备和故障链路完善定位结果以提高定位准确率。模拟结果表明提出的故障定位算法的故障检测率达到84%~95%,具有较高的故障定位可靠性。     

复杂网络大数据中重叠社区检测算法

大数据时代互联网用户数量呈爆炸性增长,社交网络、电商交易网络等复杂网络规模快速发展,准确有效地检测复杂网络大数据中重叠社区结构对用户兴趣点推荐和热点传播具有重要意义。提出一种新的面向复杂网络大数据的重叠社区检测算法DOC（Detecting Overlapping Communities over complex network big data）,时间复杂度为O（nlog²（n））,算法基于模块度聚类和图计算思想应用新的节点和边的更新方法,利用平衡二叉树对模块度增量建立索引,基于模块度最优的思想设计一种新的重叠社区检测算法。相对于传统重叠节点检测算法,对每个节点分析的频率大大降低,可以在较低的算法运行时间下获得较高的识别准确率。复杂网络大数据集上的算法测试结果表明：DOC算法能够有效地检测出网络重叠社区,社区识别准确率较高,在大规模LFR基准数据集上其重叠社区检测标准化互信息指标NMI最高能达到0.97,重叠节点检测指标F-score的平均值在0.91以上,且复杂网络大数据下的运行时间明显优于传统算法。     

公交网络下的一种费用限制最小时态路径查询索引

私人交通网络下的最短路径查询主要考虑路径长度、行驶时间等因素,而公共交通网络下的路径查询需要考虑路径上相邻的边的时间顺序约束以及路径的费用.研究了公共交通网络下3种查询：给定起点、终点、时间区间和费用上限,查找在时间区间内不超过费用上限的最早到达路径、最晚出发路径和最短耗时路径.首先给出一种Dijkstra变种算法Dijk-CCMTP,在此基础上给出3类查询的查询算法.然后提出一种高效的索引结构ACCTL（approximate cost constrained time labelling）.ACCTL采用Dijk-CCMTP对图中的每个顶点预先计算部分从该顶点出发的和到达该顶点的基本路径.对于任意从起点s到终点d的查询,可以采用类似数据库表连接的方式从ACCTL中连接从a出发的和到达d的路径生成近似解,避免遍历原图搜索路径.ACCTL建立索引的时间复杂度是O（|V|·△_max·|E|·（log|E|+△_max））,其中,|V|表示顶点数,|E|表示边数,△_max表示顶点的最大度数.实验验证ACCTL索引支持的查询速度比Dijkstra的变种算法的查询速度快2~3个数量级,并分析了影响建立索引时间和空间大小的因素.     

基于压缩的大规模图的割点求解算法

割点求解是图应用中的一个重要操作.深度优先搜索树算法可以解决割点求解问题.但是该算法存在缺点,导致它不能在实际问题中得到很好的应用.这是因为当今数据的两大特点,一是数据规模庞大,对于很多图操作提出了挑战性的要求;二是数据多变,每天数据的大量更新使得传统算法必须依据更新重复计算,浪费了时间和空间.深度优先搜索树算法的时间复杂度为O(|V|+|E|),其中,|V|和|E|分别为图的顶点的数目和边的数目.它能够很好地适应第1个特点,但是对于第2个特点该算法则无能为力.提出一种基于压缩的割点求解算法来解决这个问题.该算法通过点的朴素相似来压缩图,时间复杂度为O(|E|).在得到的无损压缩图上进行割点求解,同时在压缩图上动态地维护点和边的更新,在不解压图的情况下完成图的更新,在更新后的图上进行割点求解,极大地降低了时间和空间消耗.该压缩算法得到的压缩图对其他图操作同样适用.     

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.     

无线传感器网络中基于Top-|K|查询分布式数据重构方法

针对分簇结构或多Sink节点的无线传感器网络应用场景,提出了一种基于Top-|K|查询的分布式数据重构方法.该方法包括分布式迭代硬阈值算法和基于双阈值的分布式Top-|K|查询算法两个部分.其中,管理节点和成员节点同时运行分布式迭代硬阈值算法,以分布式方式实现迭代硬阈值计算.同时,管理节点和成员节点运行基于双阈值的分布式Top-|K|查询算法,以分布式方式实现前一算法中查询绝对值最大的前K项元素和操作.实验结果表明,该方法的数据重构性能与现有方法无明显差异,同时能够有效地减少管理节点和成员节点之间的交互次数,并且降低网络中传输的数据量.     

基于贝叶斯统计推理的故障定位实验研究

故障定位的目的是帮助程序员寻找引发失效的原因或故障位置,以加快调试过程.故障和失效间的关系往往非常复杂,难以直接描述故障到失效的转化.最新的研究多采用差异分析的方法,基于可疑模式,构建故障推理贝叶斯网络,其节点由可疑模式及组成可疑模式方法的调用者构成;定义了贝叶斯网络的构建算法、各个相关概率的定义及BBN中各个边的条件概率计算公式.提出基于该BBN的推理算法,推理得到包含故障的模块,并计算得到每个模块包含故障的概率.提出了评价方法,详细设计了参数调整与定位性能的关系实验和定位结果分析实验.实验数据表明,该故障定位方法取得了平均0.761的定准率和0.737的定全率,定位结果良好,具有较高的实用价值.     

无重叠条件严格模式匹配的高效求解算法

无重叠条件序列模式挖掘是一种间隙约束序列模式挖掘方法，与同类挖掘方法相比，该方法更容易发现有价值的频繁模式，其核心问题是计算给定模式在序列中的支持度或出现数，进而判定该模式的频繁性.而计算模式支持度问题实质是无重叠条件模式匹配.当前研究采用迭代搜索无重叠出现，然后剪枝无用结点的方式计算模式的支持度，其计算时间复杂度为O （m×m×n×W），其中，m，n和W分别为模式长度、序列长度及最大间隙.为了进一步提高无重叠条件模式匹配计算速度，从而有效地降低无重叠条件序列模式挖掘时间，提出了一种高效的算法，该算法将模式匹配问题转换为一棵网树，然后从网树的最小树根结点出发，采用回溯策略迭代搜索最左孩子方式计算无重叠最小出现，在网树上剪枝该出现后，无需进一步查找并剪枝无效结点即可实现问题的求解.理论证明了该算法的完备性，并将该算法的时间复杂度降低为O （m×n×W）.在此基础上，继续指明该问题还存在另外3种相似的求解策略，分别是从最左叶子出发迭代查找最左双亲方式、从最右树根出发迭代查找最右孩子方式和从最右叶子出发迭代查找最右双亲方式.实验结果验证了该算法的性能，特别是在序列模式挖掘中，应用该方法的挖掘算法可以降低挖掘时间.     

半动态矩形交查询算法

本文讨论了动态矩形交查询算法.文中介绍了两个半动态矩形查询的新算法，它们分别基于一维数据结构和二维数据结构.一维查询算法的查询时间复杂度是O（logM＋k′），更新时间复杂度是O（logMlogn），空间复杂度是O（nlogM/）.二维查询算法的查询时间复杂度是O（log²M＋k），更新时间复杂度是O（log²Mlogn），空间复杂度是O（nlog²M）.本文分别实现了这两个算法，通过对它们的性能进行比较，发现一维查询算法是一种高效、实用的算法.     

Computational complexity of the advancing front triangulation

An attempt to reduce the computational complexity of the advancing front triangulation is described. The method is first decomposed into subtasks, and the computational complexity is investigated separately for them. It is shown that a major subtask, namely the geometric ompatibility (mesh correctness) checks can be carried out with linear growth rate. The applied techniques include modified advancing front management, and a localization device in the form of a regular grid (stored as a hypermatrix). The other subtask (access to mesh control function) could not be made of linear computational complexity for all modes of mesh control (ad hoc and adaptive). While thead hoc gradation control yields an algorithm with ideal oveall computational complexity, the adaptive gradation control gives still a suboptimal complexity (of orderO(N logN)).     

Efficient Algorithms for the Riemann-Roch Problem and for Addition in the Jacobian of a Curve

We study the effective Riemann-Roch problem of computing a basis for the linear space L(D) associated with a divisor D on a plane curve C and its applications. Our presentation begins with an extension of Noether's algorithm for this problem to plane curves with singularities. Like the original, this algorithm has a worst-case complexity of Ω(n!^|D|), where n is the degree of the curve C.We next consider representations of divisors based on Chow forms. Using these, we produce a factorization-free polynomial-time algorithm for the effective Riemann-Roch problem, which improves the complexity of Noether's algorithm by an order of magnitude. We also present further improvements which, for curves of bounded degree, yield an algorithm with complexity which is linear in the size of the given divisor. Finally, we consider applications of this problem: to the arithmetic of the Jacobian of a plane curve, to the construction of rational functions on a curve with prescribed zeroes and poles, and to the construction of curves with prescribed intersections.     

基于矩阵和求逆及MRC的低复杂度MIMO检测器

信道编码MIMO系统需要检测器具有软输入软输出特性,而常规的检测算法通常具有很高的计算复杂度,阻碍了其在实际中的应用.提出一种低复杂度MIMO检测方案.首次迭代中,利用低复杂度快速矩阵和分解方案来获得MMSE检测输出,避免了常规矩阵和求逆中的Jordan标准型化简;其余迭代中,利用信道解码器提供的软信息将MIMO系统转...     

A Faster Algorithm for Computing the Principal Sequence of Partitions of a Graph

We consider the following problem: given an undirected weighted graph G=(V,E,c) with nonnegative weights, minimize function c(δ(Π))−λ|Π| for all values of parameter λ. Here Π is a partition of the set of nodes, the first term is the cost of edges whose endpoints belong to different components of the partition, and |Π| is the number of components. The current best known algorithm for this problem has complexity O(|V|²) maximum flow computations. We improve it to |V| parametric maximum flow computations. We observe that the complexity can be improved further for families of graphs which admit a good separator, e.g. for planar graphs.     

无线传感器网络中APIT--VP三维定位算法

在研究APIT—3D定位算法思想基础上,提出了一种改进的定位算法APIT—VP。新算法解决了APIT—3D算法在节点分布不均匀的情况下定位精度和定位覆盖率较低的问题;在一定程度上避免了PIT—3D测试中出现的OutToIn和InToOut误判错误;并且利用基于中垂面分割法代替原先的网格扫描算法,降低定位运算复杂度,减少能耗。仿真实验结果表明:在无线传感器网络环境理想、300个节点随机部署在100 m×100 m×100 m的三维区域情况下,APIT—VP算法定位覆盖率可达90%,定位误差控制在25%左右,并且与APIT—3D算法相比有效降低了计算复杂度。     

新的等价类划分算法—计数法

目前,基于基数排序的等价类划分算法有较低的时间复杂度但存在以下不足：属性值跳跃性大时会产生大量空队列;排序后仍需O（|P‖U|）的时间才实现划分,求出等价类,排序没能发挥应有作用。为此,设计了一种新算法,通过属性值映射避免大量空队列产生,通过增加一个记录等价类长度信息的计数数组,排序后仅需O（|U|）就可实现划分,求出等价类。整个算法时间复杂度为O（|C‖U|）,空间复杂度为O（|U|）,为求等价类划分提供了一个新的解决办法。     

Efficient algorithms for regular expression constrained sequence alignment

Imposing constraints is an effective means to incorporate biological knowledge into alignment procedures. As in the PROSITE database, functional sites of proteins can be effectively described as regular expressions. In an alignment of protein sequences it is natural to expect that functional motifs should be aligned together. Due to this motivation, Arslan introduced the regular expression constrained sequence alignment problem and proposed an algorithm which, if implemented naïvely, can take time and space up to O(²|Σ|⁴|V|n²) and O(²|Σ|⁴|V|n), respectively, where Σ is the alphabet, n is the sequence length, and V is the set of states in an automaton equivalent to the input regular expression. In this paper we propose a more efficient algorithm solving this problem which takes O(³|V|n²) time and O(²|V|n) space in the worst case. If |V|=O(logn) we propose another algorithm with time complexity O(²|V|log|V|n²). The time complexity of our algorithms is independent of Σ, which is desirable in protein applications where the formulation of this problem originates; a factor of ²|Σ|=400 in the time complexity of the previously proposed algorithm would significantly affect the efficiency in practice.     

A parallel sorting algorithm for a novel model of computation

The computational complexity of a parallel algorithm depends critically on the model of computation. We describe a simple and elegant rule-based model of computation in which processors apply rules asynchronously to pairs of objects from a global object space. Application of a rule to a pair of objects results in the creation of a new object if the objects satisfy the guard of the rule. The model can be efficiently implemented as a novel MIMD array processor architecture, the Intersecting Broadcast Machine. For this model of computation, we describe an efficient parallel sorting algorithm based on mergesort. The computational complexity of the sorting algorithm isO(nlog² n), comparable to that for specialized sorting networks and an improvement on theO(n ^1.5) complexity of conventional mesh-connected array processors.     

Fast exponentiation by folding the signed-digit exponent in half

For modern cryptographic systems, the public key cryptosystem such as RSA requires modular exponentiation (M ^E mod?N). The M, E and N are either as large as the 1024-bit integers or even larger, it is not a very good idea to directly compute M ^E mod?N. Recently, there are many techniques have been invented to solve the time-consuming computations of such time-consuming modular exponentiation. Among these useful algorithms, the “binary (square-and-multiply) algorithm” reduces the amount of modulo multiplications. As the “signed-digit representation algorithm” has the property of the nonzero digit occurrence probability equals to 1/3, taking this advantage, this method can more effectively decrease the amount of modular multiplications. Moreover, by using the technique of recording the common parts in the folded substrings, the “folding-exponent algorithm” can improve the efficiency of the binary algorithm, thus can further decrease the computational complexity of modular exponentiation. In this paper, a new modular exponentiation algorithm is proposed which based on the binary algorithm, signed-digit representation, and the folding-exponent technique. By using the parallel processing technique, in our proposed method, the modular multiplications and modular squaring can be executed in parallel, and thus lower down the computational complexity to k?+?3 multiplications. As modular squaring operation over GF(2 ⁿ ) is carried out by a simple cyclic right shift operation, the computational complexity of our proposed method can be further reduced to 29k/36?+?3 multiplications.