基于复合域上的椭圆曲线密码体制的计算算法

基于有限域上椭圆曲经公开密钥协议的离散对数计算算法正日益成为热点，其基本的操作是标量乘法：即用一整数乘以椭圆曲线上给定的点P。协议的主要开锁在于椭圆曲线的标量乘操作上，本文给出了3个逄法进行椭圆曲线密码系统的有效计算，第一个算法采用加－减法链的方法处理标量乘法问题；第二个算法给出了正整数n的NAF形式；第三个算法采用窗口的方法处理NAF（n）从而进一步提高加－减法链的效率，这三个算法的有机结合从银大程度上提高了椭圆曲线密码体制的加／解密速度。     

Efficient Algorithms for p-Self-Protection Problem in Static Wireless Sensor Networks

Wireless sensor networks have been widely used in many surveillance applications. Due to the importance of sensor nodes in such applications, certain level of protection need to be provided to them. We study the self protection problem for static wireless sensor networks in this paper. Self protection problem focuses on using sensor nodes to provide protection to themselves instead of the target objects or certain target area, so that the sensor nodes can resist the attacks targeting on them directly. A wireless sensor network is p-self-protected, if at any moment, for any wireless sensor (active or non-active), there are at least p active sensors that can monitor it. The problem finding minimum p-self-protection is NP-complete and no efficient self protection algorithms have been proposed. In this paper, we provide efficient centralized and distributed algorithms with constant approximation ratio for minimum p-self-protection problem in sensor networks with either homogeneous or heterogeneous sensing radius. In addition, we design efficient distributed algorithms to not only achieve p-self-protection but also maintain the connectivity of all active sensors. Our simulation confirms the performances of proposed algorithms.     

一种求解旅行商问题的高效混合遗传算法

旅行商问题(TravellingSalesmanProblemTSP)是一个典型的组合优化难题,论文提出一种求解旅行商问题的高效混合遗传算法。该算法结合遗传算法和2-opt邻域搜索优化技术,并针对旅行商问题的特点,提出K近邻点集以缩减搜索空间从而加快求解速度。基于典型实例的仿真结果表明,此算法的求解效率比较高。     

利用半点计算椭圆曲线双标量乘法算法

实现椭圆曲线密码体制最主要的运算是椭圆曲线点群上的标量乘法(或点乘)运算。一些基于椭圆曲线的密码协议比如ECDSA签名验证,就需要计算双标量乘法kP+lQ,其中P、Q为椭圆曲线点群上的任意两点。一个高效计算kP+lQ的方法就是同步计算两个标量乘法,而不是分别计算每个标量乘法再相加。通过对域F2m上的椭圆曲线双标量乘法算法进行研究,将半点公式应用于椭圆曲线的双标量乘法中,提出了一种新的同步计算双标量乘法算法,分析了效率,并与传统的基于倍点运算的双标量乘法算法进行了详细的比较,其效率更优。     

Optimal Extended Jacobian Inverse Kinematics Algorithms for Robotic Manipulators

Extended Jacobian inverse kinematics algorithms for redundant robotic manipulators are defined by combining the manipulator's kinematics with an augmenting kinematics map in such a way that the combination becomes a local diffeomorphism of the augmented taskspace. A specific choice of the augmentation relies on the optimal approximation by the extended Jacobian of the Jacobian pseudoinverse (the Moore--Penrose inverse of the Jacobian). In this paper, we propose a novel formulation of the approximation problem, rooted conceptually in the Riemannian geometry. The resulting optimality conditions assume the form of a Poisson equation involving the Laplace--Beltrami operator. Two computational examples illustrate the theory.      

Efficient Algorithms for Overlapping a Sequence of Images

In this paper, we present two novel and efficient algorithms for overlapping a sequence of quadtrees, one for binary images and the other for gray images. They relax the constraint that the common subtrees to be merged have to be at the same position and of the same size. This relaxation causes the proposed algorithm to have higher compression capability. Experiments are carried out to demonstrate the memory-saving and computational advantages of the proposed algorithm. Experimental results reveal that the proposed overlapping representation has 24.89%–54.55% (6.83%–11.71%) compression improvement and 34.92%–49.18% (24.75%–34.50%) execution-time improvement when compared to the previous result. Finally, the application of our result to overlap a sequence of gray images is presented.     

Hybrid Genetic Algorithms for a Rostering Problem

Hybrid Genetic Algorithms are described for a large-size real-life rostering problem (railway workers' job scheduling and roster optimization). The new algorithm uses an order-based representation which encodes as a chromosome the list of job units to schedule. First, a greedy algorithm is considered, which uses a randomly generated job units list, and satisfies only the constraints pertaining to the workers' job contract. Then, a genetic algorithm optimizes the global roster, minimizing its length and achieving some desired homogenizations. Finally, a second genetic algorithm (GA) is used to find the best parameter values for the first genetic algorithm. Thus, this work investigates the use of a GA together with a greedy algorithm and of a second GA to optimize the parameter values of the first GA. The results of significant tests on real data are reported. They compare favourably with the known results on Rostering Problems, both in terms of execution time and solution accuracy. This work considers a practical Rostering Problem concerning the Railway workers' rosters optimization. The size of the input data is very challenging: about 1000 duties (i.e. job-units called ‘links’) based on a large-size city location; 125 days to consider for roster optimization (summer rostering); the goal is to optimize the structure of the working-turn for any worker, and to minimize the global cost of the rosters. It should be emphasised that this is a very large problem: we will use GAs to solve the problem within an execution time in the order of a few minutes on a common workstation.     

Improved Algorithms for Partial Curve Matching

We revisit the problem of deciding whether a given curve resembles some part of a larger curve under a fixed Fréchet distance, achieving a running time of O(nm), for n and m being the number of segments in the two curves. This improves the long-standing result of Alt and Godau by an O(log(nm)) factor. Our solution is based on constructing a simple data structure which we call free-space map. Using this data structure, we obtain improved algorithms for several variants of the Fréchet distance problem, including the Fréchet distance between two closed curves, and the so-called minimum/maximum walk problems. We also improve the map matching algorithm of Alt et al. for the particular case in which the map is a directed acyclic graph.     

Approximation Algorithms for a Capacitated Network Design Problem

We study a capacitated network design problem with applications in local access network design. Given a network, the problem is to route flow from several sources to a sink and to install capacity on the edges to support the flow at minimum cost. Capacity can be purchased only in multiples of a fixed quantity. All the flow from a source must be routed in a single path to the sink. This NP-hard problem generalizes the Steiner tree problem and also more effectively models the applications traditionally formulated as capacitated tree problems. We present an approximation algorithm with performance ratio (ρ_ST + 2) where ρ_ST is the performance ratio of any approximation algorithm for the minimum Steiner tree problem. When all sources have unit demand, the ratio improves to ρ_ST + 1) and, in particular, to 2 when all nodes in the graph are sources.     

Space Efficient Algorithms for the Burrows-Wheeler Backtransformation

The Burrows-Wheeler transformation is used for effective data compression, e.g., in the well known program bzip2. Compression and decompression are done in a block-wise fashion; larger blocks usually result in better compression rates. With the currently used algorithms for decompression, 4n bytes of auxiliary memory for processing a block of n bytes are needed, 0<n<2³². This may pose a problem in embedded systems (e.g., mobile phones), where RAM is a scarce resource.     

Efficient Algorithms for the Block Hessenberg Form

We investigate in this paper the performance of parallel algorithms for computing the controllable part of a control linear system, with application to the computation of minimal realizations. Our approach is based on a method that transforms the matrices of the system to block Hessenberg form by using rank-revealing orthogonal factorizations.The experimental analysis on a high performance architecture includes two rank-revealing numerical tools: the SVD and the rank-revealing QR factorizations. Results are also reported, using the rank-revealing QR factorizations, on a parallel distributed architecture.     

Approximation Algorithms for a Capacitated Network Design Problem

We study a capacitated network design problem with applications in local access network design. Given a network, the problem is to route flow from several sources to a sink and to install capacity on the edges to support the flow at minimum cost. Capacity can be purchased only in multiples of a fixed quantity. All the flow from a source must be routed in a single path to the sink. This NP-hard problem generalizes the Steiner tree problem and also more effectively models the applications traditionally formulated as capacitated tree problems. We present an approximation algorithm with performance ratio (_ST + 2) where _ST is the performance ratio of any approximation algorithm for the minimum Steiner tree problem. When all sources have unit demand, the ratio improves to _ST + 1) and, in particular, to 2 when all nodes in the graph are sources.     

Near-Linear Time Approximation Algorithms for Curve Simplification

We consider the problem of approximating a polygonal curve P under a given error criterion by another polygonal curve P’ whose vertices are a subset of the vertices of P. The goal is to minimize the number of vertices of P’ while ensuring that the error between P’ and P is below a certain threshold. We consider two different error measures: Hausdorff and Frechet. For both error criteria, we present near-linear time approximation algorithms that, given a parameter ε > 0, compute a simplified polygonal curve P’ whose error is less than ε and size at most the size of an optimal simplified polygonal curve with error ε/2. We consider monotone curves in ℝ² in the case of the Hausdorff error measure under the uniform distance metric and arbitrary curves in any dimension for the Frechet error measure under L_p metrics. We present experimental results demonstrating that our algorithms are simple and fast, and produce close to optimal simplifications in practice.     

求解随机时变背包问题的精确算法与进化算法

随机时变背包问题(RTVKP)是一种新的动态背包问题,也是一种新的动态组合优化问题,目前它的求解算法主要是动态规划的精确算法、近似算法和遗传算法.本文首先利用动态规划提出了一个求解RTVKP问题的新精确算法,对算法时间复杂度的比较结果表明:它比已有的精确算法更适于求解背包载重较大的一类RTVKP实例.然后,分别基于差分演化和粒子群优化与贪心修正策略相结合,提出了求解RTVKP问题的两个进化算法.对5个RTVKP实例的数值计算结果比较表明: 精确算法一般不宜求解大规模的RTVKP实例,而基于差分演化、粒子群优化和遗传算法与贪心修正策略相结合的进化算法却不受实例规模与数据大小的影响,对于振荡频率大且具有较大数据的大规模RTVKP实例均能求得的一个极好的近似解.     

求解CARP-RP-ML问题的改进算法

传统方法无法有效求解交通道路维护运作中的有补给点及多装载的容量约束弧路径(CARP-RP-ML)问题。为此,提出改进的启发式算法和遗传算法。启发式算法将不同的分割算法用于由所有需求弧随机排序得到的个体上,构造问题的可行解;遗传算法利用分割算法计算其个体适应值,确定对应的可行车辆路径及补给位置,并用局部搜索作为变异算子,进一步扩大搜索空间。数值实验结果表明,与启发式算法相比,遗传算法能更有效地求解CARP-RP-ML问题。     

Efficient MFS Algorithms for Problems in Thermoelasticity

We propose efficient fast Fourier transform (FFT)-based algorithms using the method of fundamental solutions (MFS) for the numerical solution of certain problems in planar thermoelasticity. In particular, we consider problems in domains possessing radial symmetry, namely disks and annuli and it is shown that the MFS matrices arising in such problems possess circulant or block-circulant structures. The solution of the resulting systems is facilitated by appropriately diagonalizing these matrices using FFTs. Numerical experiments demonstrating the applicability of these algorithms are also presented.     

Probabilistic Algorithms for Efficient Grasping and Fixturing

Given an object with n points on its boundary where fingers can be placed, we give algorithms to select a ``strong' grasp with the least number c of fingers (up to a logarithmic factor) using several measures of goodness. Along similar lines, given an integer c , we find the ``best' κ c log c finger grasp for a small constant κ . In addition, we generalize existing measures for the case of frictionless assemblies of many objects in contact. We also give an approximation scheme which guarantees a grasp quality close to the overall optimal value where fingers are not restricted to preselected points. These problems translate into a collection of convex set covering problems where we either minimize the cover size or maximize the scaling factor of an inscribed geometric object L . We present an algorithmic framework which handles these problems in a uniform way and give approximation algorithms for specific instances of L including convex polytopes and balls. The framework generalizes an algorithm for polytope covering and approximation by Clarkson [Cla] in two different ways. Let , where d is the dimension of the Euclidean space containing L . For both types of problems, when L is a polytope, we get the same expected time bounds (with a minor improvement), and for a ball, the expected running time is for fixed d , and arbitrary positive δ . We improve this bound if we allow in addition a different kind of approximation for the optimal radius. We also give bounds when d is not a constant. Received November 14, 1996; revised June 20, 1997, and January 9, 1998.     

Algorithms for the Homogeneous Set Sandwich Problem

A homogeneous set is a non-trivial module of a graph, i.e. a non-empty, non-unitary, proper subset of a graph's vertices such that all its elements present exactly the same outer neighborhood. Given two graphs the Homogeneous Set Sandwich Problem (HSSP) asks whether there exists a sandwich graph which has a homogeneous set. In 2001 Tang et al. published an all-fast algorithm which was recently proven wrong, so that the HSSP's known upper bound would have been reset thereafter at the former determined by Cerioli et al. in 1998. We present, notwithstanding, new deterministic algorithms which have it established at We give as well two even faster randomized algorithms, whose simplicity might lend them didactic usefulness. We believe that, besides providing efficient easy-to-implement procedures to solve it, the study of these new approaches allows a fairly thorough understanding of the problem.