Efficient Rearrangement Algorithms for Shape Optimization on Elliptic Eigenvalue Problems

In this paper, several efficient rearrangement algorithms are proposed to find the optimal shape and topology for elliptic eigenvalue problems with inhomogeneous structures. The goal is to solve minimization and maximization of the k-th eigenvalue and maximization of spectrum ratios of the second order elliptic differential operator. Physically, these problems are motivated by the frequency control based on density distribution of vibrating membranes. The methods proposed are based on Rayleigh quotient formulation of eigenvalues and rearrangement algorithms which can handle topology changes automatically. Due to the efficient rearrangement strategy, the new proposed methods are more efficient than classical level set approaches based on shape and/or topological derivatives. Numerous numerical examples are provided to demonstrate the robustness and efficiency of new approach.     

Efficient Algorithms for Highly Compressed Data: The Word Problem in Generalized Higman Groups Is in P

This paper continues the 2012 STACS contribution by Diekert, Ushakov, and the author as well as the 2012 IJAC publication by the same authors. We extend the results published there in two ways. First, we show that the data structure of power circuits can be generalized to work with arbitrary bases q≥2. This results in a data structure that can hold huge integers, arising by iteratively forming powers of q. We show that the properties of power circuits known for q=2 translate to the general case. This generalization is non-trivial and additional techniques are required to preserve the time bounds of arithmetic operations that were shown for the case q=2. The extended power circuit model permits us to conduct operations in the Baumslag-Solitar group BS(1,q) as efficiently as in BS(1,2). This allows us to solve the word problem in the generalization H ₄(1,q) of Higman’s group in polynomial time. The group H ₄(1,q) is an amalgamated product of four copies of the Baumslag-Solitar group BS(1,q) rather than BS(1,2) in the original group H ₄=H ₄(1,2). As a second result, we allow arbitrary numbers f≥4 of copies of BS(1,q), leading to an even more generalized notion of Higman groups H _f (1,q). We prove that the word problem of the latter can still be solved within the \({\mathcal {O}}(n^{6})\) time bound that was shown for H ₄(1,2).     

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.     

Algorithms for Marketing-Mix Optimization

Algorithms for determining quality/cost/price tradeoffs in saturated markets are considered. A product is modeled by d real-valued qualities whose sum determines the unit cost of producing the product. This leads to the following optimization problem: given a set of n customers, each of whom has certain minimum quality requirements and a maximum price they are willing to pay, design a new product and select a price for that product in order to maximize the resulting profit.     

Efficient Algorithms for Anonymous Byzantine Agreement

This paper considers the Byzantine agreement problem in a completely connected network of anonymous processors. In this network model the processors have no identifiers and can only detect the link through which a message is delivered. We present a polynomial-time agreement algorithm that requires 3⌊(n−t)t/(n−2t)⌋+4 rounds, where n>3t is the number of processors and t is the maximal number of faulty processors that the algorithm can tolerate. We also present an early-stopping variant of the algorithm.     

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 Interface Timing Verification

This paper presents algorithms for computing separations between events that are constrained to obey prespecified relationships in their relative time of occurrence. The algorithms are useful for interface timing verification, where event separations are checked against timing requirements. The first algorithm computes separations when only linear and max constraints exist. The algorithm must converge to correct maximum separation values in a finite number of steps, or report an inconsistence of the constraints, irrespective of the existence of infinite constraint bounds or infinite event separations. It is conjectured to run in time, where V is the number of events, and E is the number of relationships between them. The other algorithms extend the first, and compute event separations in the NP-complete version of the problem where min constraints exist. Experiments demonstrate the algorithms are efficient in practice.     

RSA密码系统有效实现算法

本文提出了实现RSA算法的一种快速、适合于硬件实现的方案，在该方案中，我们作用加法链将求幂运算转化为求平方和乘法运算并大大降低了运算的次数，使用Montgomery算法将模N乘法转化为模R（基数）的算法，模R乘积的转化，以及使用一种新的数母加法器作为运算部件的基础。     

Efficient Parallel Algorithms for Planar st-Graphs

Planar st -graphs find applications in a number of areas. In this paper we present efficient parallel algorithms for solving several fundamental problems on planar st -graphs. The problems we consider include all-pairs shortest paths in weighted planar st -graphs, single-source shortest paths in weighted planar layered digraphs (which can be reduced to single-source shortest paths in certain special planar st -graphs), and depth-first search in planar st -graphs. Our parallel shortest path techniques exploit the specific geometric and graphic structures of planar st -graphs, and involve schemes for partitioning planar st -graphs into subgraphs in a way that ensures that the resulting path length matrices have a monotonicity property [1], [2]. The parallel algorithms we obtain are a considerable improvement over the previously best known solutions (when they are applied to these st -graph problems), and are in fact relatively simple. The parallel computational models we use are the CREW PRAM and EREW PRAM.     

RSA密码系统有效实现算法

大整数模幂乘运算一直是制约RSA广泛应用的瓶颈,在对传统算法剖析的基础上,提出了一种新的快速模乘算法,借鉴生成Wallace tree的思想,结合查找表和并行乘法运算进行RSA模幂运算。理论分析和试验证明新算法时间复杂度降低到O(logn)。     

Efficient Algorithms for k Maximum Sums

We study the problem of computing the k maximum sum subsequences. Given a sequence of real numbers and an integer parameter k, the problem involves finding the k largest values of for The problem for fixed k = 1, also known as the maximum sum subsequence problem, has received much attention in the literature and is linear-time solvable. Recently, Bae and Takaoka presented a -time algorithm for the k maximum sum subsequences problem. In this paper we design an efficient algorithm that solves the above problem in time in the worst case. Our algorithm is optimal for and improves over the previously best known result for any value of the user-defined parameter k < 1. Moreover, our results are also extended to the multi-dimensional versions of the k maximum sum subsequences problem; resulting in fast algorithms as well.     

Efficient Algorithms for Block-Cyclic Redistribution of Arrays

The block-cyclic data distribution is commonly used to organize array elements over the processors of a coarse-grained distributed memory parallel computer. In many scientific applications, the data layout must be reorganized at run-time in order to enhance locality and reduce remote memory access overheads. In this paper we present a general framework for developing array redistribution algorithms. Using this framework, we have developed efficient algorithms that redistribute an array from one block-cyclic layout to another. Block-cyclic redistribution consists of index set computation , wherein the destination locations for individual data blocks are calculated, and data communication , wherein these blocks are exchanged between processors. The framework treats both these operations in a uniform and integrated way. We have developed efficient and distributed algorithms for index set computation that do not require any interprocessor communication. To perform data communication in a conflict-free manner, we have developed direct indirect and hybrid algorithms. In the direct algorithm, a data block is transferred directly to its destination processor. In an indirect algorithm, data blocks are moved from source to destination processors through intermediate relay processors. The hybrid algorithm is a combination of the direct and indirect algorithms. Our framework is based on a generalized circulant matrix formalism of the redistribution problem and a general purpose distributed memory model of the parallel machine. Our algorithms sustain excellent performance over a wide range of problem and machine parameters. We have implemented our algorithms using MPI, to allow for easy portability across different HPC platforms. Experimental results on the IBM SP-2 and the Cray T3D show superior performance over previous approaches. When the block size of the cyclic data layout changes by a factor of K , the redistribution can be performed in O( log K) communication steps. This is true even when K is a prime number. In contrast, previous approaches take O(K) communication steps for redistribution. Our framework can be used for developing scalable redistribution libraries, for efficiently implementing parallelizing compiler directives, and for developing parallel algorithms for various applications. Redistribution algorithms are especially useful in signal processing applications, where the data access patterns change significantly between computational phases. They are also necessary in linear algebra programs, to perform matrix transpose operations. Received June 1, 1997; revised March 10, 1998.     

Efficient Algorithms for the Inference of Minimum Size DFAs

This work describes algorithms for the inference of minimum size deterministic automata consistent with a labeled training set. The algorithms presented represent the state of the art for this problem, known to be computationally very hard.In particular, we analyze the performance of algorithms that use implicit enumeration of solutions and algorithms that perform explicit search but incorporate a set of techniques known as dependency directed backtracking to prune the search tree effectively.We present empirical results that show the comparative efficiency of the methods studied and discuss alternative approaches to this problem, evaluating their advantages and drawbacks.     

Satisfiability-Based Algorithms for Boolean Optimization

This paper proposes new algorithms for the Binate Covering Problem (BCP), a well-known restriction of Boolean Optimization. Binate Covering finds application in many areas of Computer Science and Engineering. In Artificial Intelligence, BCP can be used for computing minimum-size prime implicants of Boolean functions, of interest in Automated Reasoning and Non-Monotonic Reasoning. Moreover, Binate Covering is an essential modeling tool in Electronic Design Automation. The objectives of the paper are to briefly review branch-and-bound algorithms for BCP, to describe how to apply backtrack search pruning techniques from the Boolean Satisfiability (SAT) domain to BCP, and to illustrate how to strengthen those pruning techniques by exploiting the actual formulation of BCP. Experimental results, obtained on representative instances indicate that the proposed techniques provide significant performance gains for a large number of problem instances.     

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.     

兄弟轴的有效楼梯连接算法

使用关系数据库来存储和查询XML数据是很多人正在研究的问题.其中,楼梯连接是这一方向的重要工作.楼梯连接是作为对RDBMS内核的局部改进而提出来的,它封装了提高XPath处理性能所需的树结构知识.研究了兄弟关系的楼梯连接算法问题.基于区间编码方案,提出了两个有效的楼梯连接算法来计算兄弟关系.这两个算法具有如下特点:不参与连接的节点可以根据B+树索引事先判断出来并跳过,上下文节点表和文档表都最多扫描一次,按文档序有序输出结果.实验结果验证了算法的高效性.普遍认为,这是首次对这一问题进行的研究.     

Simple Efficient Load-Balancing Algorithms for Peer-to-Peer Systems

Load balancing is a critical issue for the efficient operation of peer-to-peer (P2P) networks. We give two new load-balancing protocols whose provable performance guarantees are within a constant factor of optimal. Our protocols refine the consistent hashing data structure that underlies the Chord (and Koorde) P2P network. Both preserve Chord's logarithmic query time and near-optimal data migration cost. Consistent hashing is an instance of the distributed hash table (DHT) paradigm for assigning items to nodes in a P2P system: items and nodes are mapped to a common address space, and nodes have to store all items residing closeby in the address space. Our first protocol balances the distribution of the key address space to nodes, which yields a load-balanced system when the DHT maps items "randomly" into the address space. To our knowledge, this yields the first P2P scheme simultaneously achieving O(log n) degree, O(log n) look-up cost, and constant-factor load balance (previous schemes settled for any two of the three). Our second protocol aims to balance directly the distribution of items among the nodes. This is useful when the distribution of items in the address space cannot be randomized. We give a simple protocol that balances load by moving nodes to arbitrary locations "where they are needed." As an application, we use the last protocol to give an optimal implementation of a distributed data structure for range searches on ordered data.     

Space Efficient Algorithms for Ordered Tree Comparison

In this paper we present techniques to significantly improve the space complexity of several ordered tree comparison algorithms without sacrificing the corresponding time complexity. We present new algorithms for computing the constrained ordered tree edit distance and the alignment of (ordered) trees. The techniques can also be applied to other related problems.