Compact directed acyclic word graphs for a sliding window

Suffix trees are a well-known and widely-studied data structure highly useful for string matching. The suffix tree of a string w can be constructed in O(n) time and space, where n denotes the length of w. Larsson achieved an efficient algorithm to maintain suffix trees for a sliding window. It contributes to prediction by partial matching (PPM) style statistical data compression scheme. Compact directed acyclic word graphs (CDAWGs) are a more space-economical data structure for indexing strings. In this paper we propose a linear-time algorithm to maintain CDAWGs for a sliding window.     

The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

Towards the Exact Minimization of BDDs—An Elitism-Based Distributed Evolutionary Algorithm

Binary Decision Diagrams (BDDs) are the state-of-the-art data structure for representation and manipulation of Boolean functions. In general, exact BDD minimization is NP-complete. For BDD-based technology, a small improvement in the number of nodes often simplifies the follow-up problem tremendously. This paper proposes an elitism-based evolutionary algorithm (EBEA) for BDD minimization. It can efficiently find the optimal orderings of variables for all LGSynth91 benchmark circuits with a known minimum size. Moreover, we develop a distributed model of EBEA, DEBEA, which obtains the best-ever variable orders for almost all benchmarks in the LGSynth91. Experimental results show that DEBEA is able to achieve super-linear performance compared to EBEA for some hard benchmarks.     

Combining Swaps and Node Weights in an Adaptive Greedy Approach for the Maximum Clique Problem

In this work, the NP-hard maximum clique problem on graphs is considered. Starting from basic greedy heuristics, modifications and improvements are proposed and combined in a two-phase heuristic procedure. In the first phase an improved greedy procedure is applied starting from each node of the graph; on the basis of the results of this phase a reduced subset of nodes is selected and an adaptive greedy algorithm is repeatedly started to build cliques around such nodes. In each restart the selection of nodes is biased by the maximal clique generated in the previous execution. Computational results are reported on the DIMACS benchmarks suite. Remarkably, the two-phase procedure successfully solves the difficult Brockington-Culberson instances, and is generally competitive with state-of-the-art much more complex heuristics.     

Widrow-cellular neural network and optoelectronic implementation

A new type of optoelectronic cellular neural network has been developed by providing the capability of coefficients adjusment of cellular neural network (CNN) using Widrow based perceptron learning algorithm. The new supervised cellular neural network is called Widrow-CNN. Despite the unsupervised CNN, the proposed learning algorithm allows to use the Widrow-CNN for various image processing applications easily. Also, the capability of CNN for image processing and feature extraction has been improved using basic joint transform correlation architecture. This hardware application presents high speed processing capability compared to digital applications. The optoelectronic Widrow-CNN has been tested for classic CNN feature extraction problems. It yields the best results even in case of hard feature extraction problems such as diagonal line detection and vertical line determination.     

Randomization helps to perform independent tasks reliably

This paper is about algorithms that schedule tasks to be performed in a distributed failure‐prone environment, when processors communicate by message‐passing, and when tasks are independent and of unit length. The processors work under synchrony and may fail by crashing. Failure patterns are imposed by adversaries. Linearly‐bounded adversaries may fail up to a constant fraction of the processors. Weakly‐adaptive adversaries have to select, prior to the start of an execution, a subset of processors to be failure‐prone, and then may fail only the selected processors, at arbitrary steps, in the course of the execution. Strongly adaptive adversaries have a total number of failures as the only restriction on failure patterns. The measures of complexity are work, measured as the available processor steps, and communication, measured as the number of point‐to‐point messages. A randomized algorithm is developed, that attains both ??(n log*n) expected work and ??(n log*n) expected communication, against weakly‐adaptive linearly‐bounded adversaries, in the case when the numbers of tasks and processors are both equal to n. This is in contrast with performance of algorithms against strongly‐adaptive linearly‐bounded adversaries, which has to be Ω(n log n/log log n) in terms of work. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Approximation bounds for quadratic maximization and max-cut problems with semidefinite programming relaxation

In this paper,we consider a class of quadratic maximization problems.For a subclass of the problems,we show that the SDP relaxation approach yields an approximation solution with the ratio is dependent on the data of the problem with α being a uniform lower bound.In light of this new bound,we show that the actual worst-case performance ratio of the SDP relaxation approach (with the triangle inequalities added) is at least α δd if every weight is strictly positive,where δd ＞ 0 is a constant depending on the problem dimension and data.     

Fitting the control parameters of a genetic algorithm: An application to technical trading systems design

This paper studies the problem of how changes in the design of the genetic algorithm (GA) have an effect on the results obtained in real-life applications. In this study, focused on the application of a GA to the tuning of technical trading rules in the context of financial markets, our tentative thesis is that the GA is robust with respect to design changes. The optimization of technical trading systems is a suitable area for the application of the GA metaheuristic, as the complexity of the problem grows exponentially as new technical rules are added to the system and as the answer time is crucial when applying the system to real-time data. Up to now, most of GAs applications to this subject obviated the question of possible “design dependence” in their results. The data we report, based on our experiments, do not allow us to refute the hypothesis of robustness of the GA to design implementation, when applying to technical trading systems tuning.     

光传送网中结合传输损伤的路由和波长分配

在波长路由光网优化设计的过程中考虑了物理传输损伤造成的限制,提出了一种联合优化思路.将光信号在传输过程中的物理损伤作为问题公式的另一维约束,给出了相应的启发式算法,并按照由粗到细的机制对所提出的思路做了相应的评估,同时对负荷平衡问题作了初步的分析.数值结果表明这种算法可以获得与优化值相近的波长需求解,并且能够保证网络的传输性能,其业务分布随着备选路径的增加而趋向均衡.     

A parallel version of the preconditioned conjugate gradient method for boundary element equations

The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems.