无人值守传感器网络的低通信成本存储算法

针对无人值守传感器网络的数据存储问题, 提出了一种低通信成本的分布式数据存储算法。算法采用步数为cn的定向随机游走机制, 将网络中的k个源数据包按照一定的接收概率分散存储到了网络中所有的n个节点, 在每个节点形成了一个存储数据包。实验表明, 基于该算法的存储过程完成之后, 即使有部分传感器节点损坏, sink节点只要随机收集到k+ε（ε≥10）个存储数据包, 就能成功计算出原来的k个源数据包。与具有代表性的基于LT码方法相比, 该算法在节约sink节点访问成本的同时, 也将网络的通信时间复杂度从O(n　ln　n)降到了O(n), 具有良好的应用潜质。     

基因组Translocation排序问题的改进多项式算法

该文给出基因组Transhocation排序问题的一个改进多项式算法，原算法所有存储空间O（n)，时间复杂度为O(n^3)，文中改进算法仍采用O(n)存储空间，时间复杂度为O(n^2logn),具体地，将计算Translocation距离的时间复杂度由O(n^3)改进为O(n^2),将计算Translocation序列的时间复杂度由O(n^3)改进为O(n^2logn).     

基于蜂窝结构的传感器网络覆盖问题求解算法

在无线传感器网络中,求解能够完全覆盖目标区域的最小覆盖集是个NP难问题.在传感器节点数目较多时,目前只能通过近似算法求解.蜂窝结构是覆盖二维平面的最佳拓扑结构,但不能直接用于求解无线传感器网络的覆盖问题.提出了一种基于蜂窝结构的覆盖问题求解算法,在该算法迭代求解过程的每一阶段,选出一个节点加入到初始为空的节点集合中,并使得该节点集合的拓扑结构接近于蜂窝结构,直至该节点集合成为覆盖集.该算法在最坏情况下的时间复杂度为O(n3),这里n为传感器节点总数.实验结果表明该算法可在很短的时间内执行完,在所得覆盖集的大小方面要优于现有的覆盖问题求解算法.     

快速动态优先搜索树的实现及其应用

对形如（x1：x2,[-∞：y]）的二维查询问题,提出一种快速的、易于实现的动态优先搜索树数据结构及其相关算法,采用只在叶节点存储数据的结构,以及在常数时间内实现旋转操作的算法。设n为数据点的个数,k为满足搜索条件的解的个数,则该动态搜索树空间复杂度为O（n）,插入、删除操作的时间复杂度为O（10gn）,搜索复杂度为O（logn＋k）。     

具有大量错误结点的超立方体网络中并行路由算法

本文讨论具有大量错误结点的超立方体网络中的并行路由算法。假定Hn是一个局部k-维子立方体连通用的n-维超立方体网络,本文提出的并行路由算法能够找出至少K=min（Dk(u),Dk(v）条并行路径,其中每一条路径的长度不超过（dH(Uk,Vk）＋3）2^k。该算法的时间复杂度为O（Kn2^k）。这里,Dk(u）和Dk(v）分别代表源结点u和目的结点v的正确的邻结点个数（不考虑u和v所在的k－维子立方体内部的邻结点）,dH(Uk,Vk）代表源结点u和目的结点v所在的两个k－维子立方体Uk和Vk之间的海明距离。本文还考察了了k=3的特殊情况,在k=3并且有分别不超过12．5％和25％的错误结点的情况下,该算法的时间复杂度为O（Kn）,并且每一条路径的路径长度分别在大约1．5和2倍源结点和目的结点之间的海明距离之内。该算法只要求结点知道其邻结点的状态,而无需知道整个网络信息,也就是说,该算法是基于局部信息的,因而该算法具有很强的实际意义。     

线对象邻接关系快速重构算法

给定向量化坐标,计算n个线对象两两邻接关系,普通算法时间复杂度为O(n*n);理论最好时间复杂度为O(C),其中C是邻接关系的基数。基于散列桶,给出了建立线对象邻接关系的快速算法,其平均时间复杂度为O(n(1+1/r)),r为算法分配的桶数量与n的比,空间复杂度为O(n)。证明了若不允许使用额外空间,则不可能使用排序算法解决该问题;给出了允许使用额外空间条件下的两遍排序算法,时间复杂度为O(n(lbn+1+2/r))。应用表明快速算法比普通算法速度提高1~3个数量级。     

有向传感器网络中基于概率感知模型的最小连通k覆盖集算法

无线传感器网络的基本问题之一是,网络节点如何利用有限的能量对人们所关注的物理世界进行满意的监测,这可抽象为最小连通k覆盖集问题。传统的最小连通k覆盖集问题是基于确定型全向感知模型的,该模型过于理想化,不能适用于复杂的应用环境,也不能应用于有向传感器网络中。针对上述局限,本文提出了有向传感器网络中基于概率感感知模型的最小连通k覆盖集问题（MCKS）,并指出这是NP难问题;设计了基于0-1整数规划和最小生成树的集中式近 BDA）,分别证明两种算法最终得到的是MCKS问题的可行解,并分析了算法的时间复杂度、性能比和通信复杂度。通过仿真实验并与ILP算法和BGA算法进行比较的结果表明： 在基于概率感知模型的条件下,IPA和CBDA能够有效实现有向传感器网络中的连通k覆盖,并且激活节点数目较少,网络寿命延长。     

三维服装仿真中的"服装-人体"快速冲突检测及响应算法

维胆装仿真可以为三维人体动画生成逼真的服装动态效果，但其中的冲突检测与仿真计算的时间复杂度太高，其实用性一直受到很大限制．提出了一种快速的“服装-人体”冲突检测友响应算法，在人体运动状态下，快速检测服装与人体之间的位置冲突，其时间复杂度仅为O（n）（n为服装模型上的顶点数目）．在此基础上，提出一种合理有效的冲突响应机制，并实现快速稳定的三维服装仿真，取得了真实的仿真结果．     

一种新的交叉立方体最短路径路由算法

Efe提出的交叉立方体(crossed cube)是超立方体(hypercube)的一种变型.交叉立方体的某些性质优于超立方体,比如其直径几乎是超立方体的一半.Efe提出了时间复杂度为O(n2)的交叉立方体最短路径路由算法.Chang等人扩展了Efe的算法,时间复杂度为O(n),它在路由的每一步有更多条边作为最短路径可供寻路选择.但这些边并没有包含全部可进行最短路径路由的边.文中给出了结点各边可进行最短路径路由的充要条件,并在此基础上提出了一种时间复杂度为O(n2)的交叉立方体最短路径路由算法,它在路由的每一步都将所有的最短路径边作为候选边.理论分析和实例表明它可输出任意一条最短路径.     

超平面覆盖问题的参数化改进算法

超平面覆盖问题是计算几何领域中一类典型的NP难问题,在实际生活中有着广泛的应用.针对NP难问题的难解性,人们提出了一些传统的方法用来求解这些NP难问题.但由于这些方法具有各自的局限性,不能满足实际应用中的各种需求,人们从新的理论角度为固定参数可解的NP难问题设计参数算法.通过深入分析直线覆盖问题(超平面覆盖问题的一个特例)的结构特征,并利用深度有界搜索树的方法,提出了一个时间复杂度为O(k3(0.736k)k+nlogk)的确定性参数算法,极大地改进了当前最好的结果O((k/2.2)2k+nlogk).通过对上述算法在高维空间中的进一步扩展,提出了关于超平面覆盖问题时间复杂度为O(dkd+1(dk)!/((d!)kk!)+nd+1)确定性参数算法,对当前的最好结果O(kd(k+1)+nd+1)有较大改进.     

Maximizing lifetime in wireless sensor networks with multiple sensor families

Wireless sensor networks are generally composed of a large number of hardware devices of the same type, deployed over a region of interest in order to perform a monitoring activity on a set of target points. Nowadays, several different types of sensor devices exist, which are able to monitor different aspects of the region of interest (including sound, vibrations, proximity, chemical contaminants, among others) and may be deployed together in a heterogeneous network. In this work, we face the problem of maximizing the amount of time during which such a network can remain operational, while maintaining at all times a minimum coverage guarantee for all the different sensor types. Some global regularity conditions in order to guarantee a fair level of coverage for each sensor type to each target are also taken into account in a second variant of the proposed problem. For both problem variants we developed an exact approach, which is based on a column generation algorithm whose subproblem is either solved heuristically by means of a genetic algorithm or optimally by an appropriate ILP formulation. In our computational tests the proposed genetic algorithm is shown to be able to dramatically speed up the procedure, enabling the resolution of large-scale instances within reasonable computational times.     

Efficient algorithms for globally optimal trajectories

We present serial and parallel algorithms for solving a system of equations that arises from the discretization of the Hamilton-Jacobi equation associated to a trajectory optimization problem of the following type. A vehicle starts at a prespecified point x_o and follows a unit speed trajectory x(t) inside a region in ℛ^m until an unspecified time T that the region is exited. A trajectory minimizing a cost function of the form ∫₀^T r(x(t))dt+q(x(T)) is sought. The discretized Hamilton-Jacobi equation corresponding to this problem is usually solved using iterative methods. Nevertheless, assuming that the function r is positive, we are able to exploit the problem structure and develop one-pass algorithms for the discretized problem. The first algorithm resembles Dijkstra's shortest path algorithm and runs in time O(n log n), where n is the number of grid points. The second algorithm uses a somewhat different discretization and borrows some ideas from a variation of Dial's shortest path algorithm (1969) that we develop here; it runs in time O(n), which is the best possible, under some fairly mild assumptions. Finally, we show that the latter algorithm can be efficiently parallelized: for two-dimensional problems and with p processors, its running time becomes O(n/p), provided that p=O(√n/log n)     

A coverage algorithm for multiple autonomous surface vehicles in flowing environments

This paper is concerned with the coverage problem with multiple autonomous surface vehicles (ASVs) in time-varying flowing environment, where the interest information distribution is unknown to the coverage networks. While taking the model parameter uncertainty into consideration, a decentralized, adaptive control law is proposed such that the coverage network will converge to the optimal assigned region from arbitrary positions. For ease of exploration, we first investigate the static coverage problem of two-agent systems in flowing environment and present an example by extending the two-agent systems into the general case. In addition, Gaussian Estimation is introduced to predict the value of the sensory function through the sampled measurements. By using the static coverage partition as theoretical foundation, we transform the optimal coverage control into the moving target tracking problems, where the target is the centroid of the assigned region for each ASV. Based on these techniques, a decentralized kinematic control algorithm is developed to navigate the multi-ASV systems. Furthermore, the adaptive back-stepping techniques are employed to extend the kinematic controller into dynamic case with uncertain model parameters. Finally, simulation studies are provided to demonstrate the feasibility and effectiveness of the proposed approaches.     

一种可重构阵列的最小瑕点覆盖算法

关于可重构阵列的瑕点覆盖问题受到了很多文献的关注，特别地，关于可重构阵列的最小瑕点覆盖问题等价于二分图的受约束最小点覆盖问题，并被证明是NP-完全问题。针对本问题提出的算法运行时间为O(1．19^k kn)，这里k为可替换行与列的数目，改进了原有的最好结果，其运行时间为0(1．266k kn)，较好地组合并扩展了研究参数计算的最新技术与经典匹配理论，且具有较好的实用价值。这是关于可重构阵列的最小瑕点覆盖问题算法又一较大的改进，也是目前最小点覆盖问题相关参数算法的较有意义的改进。     

Online Maintenance of k-Medians and k-Covers on a Line

The standard dynamic programming solution to finding k-medians on a line with n nodes requires O(kn²) time. Dynamic programming speed-up techniques, e.g., use of the quadrangle inequality or properties of totally monotone matrices, can reduce this to O(kn) time. However, these speed-up techniques are inherently static and cannot be used in an online setting, i.e., if we want to increase the size of the problem by one new point. Then, in the worst case, we could do no better than recalculating the solution to the entire problem from scratch in O(kn) time. The major result of this paper is to show that we can maintain the dynamic programming speed up in an online setting where points are added from left to right on a line. Computing the new k-medians after adding a new point takes only O(k) amortized time and O(k log n) worst-case time (simultaneously). Using similar techniques, we can also solve the online k-coverage with uniform coverage on a line problem with the same time bounds.     

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     

基于三维限制区域生长的SD-OCT中浆NRD病变区域分割

中浆(CSC)病变区域的大小对于病变的诊断及研究有着关键的作用,而视网膜神经上皮层脱离(NRD)形态在中浆病变中最为普遍且病变程度最为严重,因此快速准确地分割出NRD病变区域十分重要。给出一种全自动的频域光学相干断层(SD-OCT)中浆NRD病变分割方法。首次在三维空间进行NRD病变分割,将二维图像上的病变区域分割问题转化为三维空间的体分割问题,充分利用了数据的三维结构信息,提高了分割精度。18组中浆NRD病变的SD-OCT图像的实验结果表明:该算法能够准确分割出中浆NRD病变,且平均覆盖率高达89.5%。与其他4种分割方法相比,所提方法精度最高且耗时最短,在临床应用与研究中具有极大的优势。     

Allocating tree structured programs in a distributed system withuniform communication costs

Studies the complexity of the problem of allocating m modules to n processors in a distributed system to minimize total communication and execution costs. When the communication graph is a tree, Bokhari has shown that the optimum allocation can be determined in O(mn²) time. Recently, this result has been generalized by Fernandez-Baca, who has proposed an allocation algorithm in O(mn^k+1) when the communication graph is a partial k-tree. The author shows that in the case where communication costs are uniform, the module allocation problem can be solved in O(mn) time if the communication graph is a tree. This algorithm is asymptotically optimum     

Dynamic Programming on the Word RAM

Dynamic programming is one of the fundamental techniques for solving optimization problems. In this paper we propose a general framework which can be used to decrease the time and space complexity of these algorithms with a logarithmic factor. The framework is based on word encoding, i.e. by representing subsolutions as bits in an integer. In this way word parallelism can be used in the evaluation of the dynamic programming recursion. Using this encoding the subset-sum problem can be solved in O( n b/ log b) time and O(b/ log b) space, where n is the number of integers given and b is the target sum. The knapsack problem can be solved in O( n m/ log m) time and O(m/ log m) space, where n is the number of items and m = max{b,z} is the maximum of the capacity b and the optimal solution value z . The problem of finding a path of a given length b in a directed acyclic graph G=(V,E) can be solved in O(|E|b/ log b) time and O(|V|b/ log b) space. Several other examples are given showing the generality of the achieved technique. Extensive computational experiments are provided to demonstrate that the achieved results are not only of theoretical interest but actually lead to algorithms which are up to two orders of magnitude faster than their predecessors. This is a surprising observation as the increase in speed is larger than the word size of the processor.     

Multi-agent coverage control design with dynamic sensing regions

A cooperative region reconnaissance problem is considered in this paper where a group of agents are required to reconnoitre a region of interest. A main challenge of this problem is the sensing region of each agent varies with its altitude within an altitude constraint. Meanwhile, the reconnaissance ability of an agent is determined by its altitude and radial distance. First, the region reconnaissance is formulated as an effective coverage problem, which means that each point in the given region should be surveyed until a preset level is achieved. Then, an effective coverage control law is proposed to minimize coverage performance index by adjusting the altitude of an agent. Finally, the effectiveness of the proposed control law is verified through numerical simulations.