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Teaching Reform and Practice of Algorithm Design and Analysis Course
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作者 Kejia Zhang Haiwei Pan +3 位作者 Zhiqiang Ma Shaoqiang Zhu Yingxin Qin Lan Zhang 《国际计算机前沿大会会议论文集》 2025年第1期140-149,共10页
This paper reforms the shortcomings and difficulties in the teaching process of the“Algorithm Design and Analysis”course.The knowledge graph optimizes the teaching content,abandons the traditional teaching method,ca... This paper reforms the shortcomings and difficulties in the teaching process of the“Algorithm Design and Analysis”course.The knowledge graph optimizes the teaching content,abandons the traditional teaching method,captures the direction of talent demand,adjusts the class time allocation,reorganizes the assessment method,focuses on practical hands-on ability,and designs a multistage teaching quality evaluation system to promote the overall improvement of teaching quality.The practice of course reform has proven that the“Algorithm Design and Analysis”course has achieved good teaching results after a series of teaching reform measures. 展开更多
关键词 algorithm design analysis Teaching Reform Talent Cultivation
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Using Large Language Models to Promote Vocational Skills Improvement:Reform and Practice of the“Algorithm Design and Analysis”Course in Higher Education
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作者 Kejia Zhang Haiwei Pan +3 位作者 Zhiqiang Ma Shaoqiang Zhu Xiaoliang Qin Lan Zhang 《国际计算机前沿大会会议论文集》 2025年第1期150-159,共10页
“Algorithm Design and Analysis”is not only one of the important courses in the undergraduate teaching of computer science and technology but also a key part of computer professional skills.In recent years,with the r... “Algorithm Design and Analysis”is not only one of the important courses in the undergraduate teaching of computer science and technology but also a key part of computer professional skills.In recent years,with the rise and widespread application of big language models,many teaching reform plans have been produced to promote the quality and efficiency of teaching.This paper studies how to refer to software development professional skills standards,investigates the knowledge points of“Algorithm Design and Analysis”courses in other educational institutions,uses cutting-edge core technology big language models to drive the improvement of teaching evaluation methods,improves teaching efficiency,and carries out reforms and practices in teaching content for undergraduate students in computer science. 展开更多
关键词 algorithm design and analysis Large Language Model Professional Skill Standards Teaching Reform
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Analysis method and algorithm design of biological sequence problem based on generalized k-mer vector
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作者 LIU Wen-li WU Qing-biao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2021年第1期114-127,共14页
K-mer can be used for the description of biological sequences and k-mer distribution is a tool for solving sequences analysis problems in bioinformatics.We can use k-mer vector as a representation method of the k-mer ... K-mer can be used for the description of biological sequences and k-mer distribution is a tool for solving sequences analysis problems in bioinformatics.We can use k-mer vector as a representation method of the k-mer distribution of the biological sequence.Problems,such as similarity calculations or sequence assembly,can be described in the k-mer vector space.It helps us to identify new features of an old sequence-based problem in bioinformatics and develop new algorithms using the concepts and methods from linear space theory.In this study,we defined the k-mer vector space for the generalized biological sequences.The meaning of corresponding vector operations is explained in the biological context.We presented the vector/matrix form of several widely seen sequence-based problems,including read quantification,sequence assembly,and pattern detection problem.Its advantages and disadvantages are discussed.Also,we implement a tool for the sequence assembly problem based on the concepts of k-mer vector methods.It shows the practicability and convenience of this algorithm design strategy. 展开更多
关键词 vector space biological sequence k-mer algorithm design analysis method.
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A New Rational-based Optimal Design Strategy of Ship Structure Based on Multi-level Analysis and Super-element Modeling Method 被引量:6
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作者 Li Sun Deyu Wang 《Journal of Marine Science and Application》 2011年第3期272-280,共9页
A new multi-level analysis method of introducing the super-element modeling method, derived from the multi-level analysis method first proposed by O. F. Hughes, has been proposed in this paper to solve the problem of ... A new multi-level analysis method of introducing the super-element modeling method, derived from the multi-level analysis method first proposed by O. F. Hughes, has been proposed in this paper to solve the problem of high time cost in adopting a rational-based optimal design method for ship structural design. Furthermore,the method was verified by its effective application in optimization of the mid-ship section of a container ship. A full 3-D FEM model of a ship,suffering static and quasi-static loads, was used as the analyzing object for evaluating the structural performance of the mid-ship module, including static strength and buckling performance. Research results reveal that this new method could substantially reduce the computational cost of the rational-based optimization problem without decreasing its accuracy, which increases the feasibility and economic efficiency of using a rational-based optimal design method in ship structural design. 展开更多
关键词 rational-based optimal design method (RBODM) multi-level analysis SUPER-ELEMENT ship module genetic algorithm
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Universally Composable Symbolic Analysis of Group Key Exchange Protocol
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作者 张子剑 祝烈煌 廖乐健 《China Communications》 SCIE CSCD 2011年第2期59-65,共7页
Canetti and Herzog have already proposed universally composable symbolic analysis(UCSA) to analyze mutual authentication and key exchange protocols. However,they do not analyze group key exchange protocol. Therefore,t... Canetti and Herzog have already proposed universally composable symbolic analysis(UCSA) to analyze mutual authentication and key exchange protocols. However,they do not analyze group key exchange protocol. Therefore,this paper explores an approach to analyze group key exchange protocols,which realize automation and guarantee the soundness of cryptography. Considered that there exist many kinds of group key exchange protocols and the participants’ number of each protocol is arbitrary. So this paper takes the case of Burmester-Desmedt(BD) protocol with three participants against passive adversary(3-BD-Passive) . In a nutshell,our works lay the root for analyzing group key exchange protocols automatically without sacrificing soundness of cryptography. 展开更多
关键词 universally composable symbolic analysis universally composable mapping algorithm burmester-desmedt protocol group key exchange protocol
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Stability analysis of underground engineering based on multidisciplinary design optimization
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作者 马荣 周科平 高峰 《Journal of Coal Science & Engineering(China)》 2008年第4期608-612,共5页
Aiming at characteristics of underground engineering,analyzed the feasibility of Multidisciplinary Design Optimization (MDO) used in underground engineering,and put forward a modularization-based MDO method and the id... Aiming at characteristics of underground engineering,analyzed the feasibility of Multidisciplinary Design Optimization (MDO) used in underground engineering,and put forward a modularization-based MDO method and the idea of MDO to resolve problems in stability analysis,proving the validity and feasibility of using MDO in underground engi- neering.Characteristics of uncertainty,complexity and nonlinear become bottle-neck to carry on underground engineering stability analysis by MDO.Therefore,the application of MDO in underground engineering stability analysis is still at a stage of exploration,which need some deep research. 展开更多
关键词 underground engineering multidisciplinary design optimization (MDO) stability analysis optimum algorithm
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Optimal design of pressure vessel using an improved genetic algorithm 被引量:5
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作者 Peng-fei LIU Ping XU +1 位作者 Shu-xin HAN Jin-yang ZHENG 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2008年第9期1264-1269,共6页
As the idea of simulated annealing (SA) is introduced into the fitness function, an improved genetic algorithm (GA) is proposed to perform the optimal design of a pressure vessel which aims to attain the minimum weigh... As the idea of simulated annealing (SA) is introduced into the fitness function, an improved genetic algorithm (GA) is proposed to perform the optimal design of a pressure vessel which aims to attain the minimum weight under burst pressure con- straint. The actual burst pressure is calculated using the arc-length and restart analysis in finite element analysis (FEA). A penalty function in the fitness function is proposed to deal with the constrained problem. The effects of the population size and the number of generations in the GA on the weight and burst pressure of the vessel are explored. The optimization results using the proposed GA are also compared with those using the simple GA and the conventional Monte Carlo method. 展开更多
关键词 Pressure vessel Optimal design Genetic algorithm (GA) Simulated annealing (SA) Finite element analysis (FEA)
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Real-time Design Constraints in Implementing Active Vibration Control Algorithms 被引量:1
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作者 Mohammed Alamgir Hossain Mohammad Osman Tokhi 《International Journal of Automation and computing》 EI 2006年第3期252-262,共11页
Although computer architectures incorporate fast processing hardware resources, high performance real-time implementation of a complex control algorithm requires an efficient design and software coding of the algorith... Although computer architectures incorporate fast processing hardware resources, high performance real-time implementation of a complex control algorithm requires an efficient design and software coding of the algorithm so as to exploit special features of the hardware and avoid associated architecture shortcomings. This paper presents an investigation into the analysis and design mechanisms that will lead to reduction in the execution time in implementing real-time control algorithms. The proposed mechanisms are exemplified by means of one algorithm, which demonstrates their applicability to real-time applications. An active vibration control (AVC) algorithm for a flexible beam system simulated using the finite difference (FD) method is considered to demonstrate the effectiveness of the proposed methods. A comparative performance evaluation of the proposed design mechanisms is presented and discussed through a set of experiments. 展开更多
关键词 algorithm analysis and design active vibration control (AVC) flexible beam system real-time control memory management.
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CONSTRUCTION METHODS AND ALGORITHM DESIGN OF WAVELET BASES
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作者 李兵兵 常义林 胡征 《Journal of Electronics(China)》 1995年第2期181-185,共5页
Based on the brief introduction of the principles of wavelet analysis, this paper gives a summary of several typical wavelet bases from the point of view of perfect reconstruction of signals and emphasizes that design... Based on the brief introduction of the principles of wavelet analysis, this paper gives a summary of several typical wavelet bases from the point of view of perfect reconstruction of signals and emphasizes that designing wavelet bases which are used to decompose the signal into a two-band form is equivalent to designing a two-band filter bank with perfect or nearly perfect property. The generating algorithm corresponding to Daubechies bases and some simulated results are also given in the paper. 展开更多
关键词 WAVELET analysis BASES design algorithm CONSTRUCTION
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Optimal Design of Tapered Roller Bearings Based on Multi⁃Physics Objectives Using Evolutionary Algorithms
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作者 Rajiv Tiwari Rahul M.P.Chandran 《Journal of Harbin Institute of Technology(New Series)》 CAS 2023年第1期73-84,共12页
Rolling element bearing is the most common machine element in rotating machinery.An extended life is among the foremost imperative standards in the optimal design of rolling element bearings,which confide on the fatig... Rolling element bearing is the most common machine element in rotating machinery.An extended life is among the foremost imperative standards in the optimal design of rolling element bearings,which confide on the fatigue failure,wear,and thermal conditions of bearings.To fill the gap,in the current work,all three objectives of a tapered roller bearing have been innovatively considered respectively,which are the dynamic capacity,elasto-hydrodynamic lubrication(EHL)minimum film⁃thickness,and maximum bearing temperature.These objective function formulations are presented,associated design variables are identified,and constraints are discussed.To solve complex non⁃linear constrained optimization formulations,a best⁃practice design procedure was investigated using the Artificial Bee Colony(ABC)algorithms.A sensitivity analysis of several geometric design variables was conducted to observe the difference in all three objectives.An excellent enhancement was found in the bearing designs that have been optimized as compared with bearing standards and previously published works.The present study will definitely add to the present experience based design followed in bearing industries to save time and obtain assessment of bearing performance before manufacturing.To verify the improvement,an experimental investigation is worthwhile conducting. 展开更多
关键词 dynamic capacity evolutionary algorithm optimum design tapered roller bearings TEMPERATURE tolerance analysis
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Structural Reliability Analysis Based on Differential Evolution Algorithm and Hypersphere Integration
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作者 CHEN Zhenzhong HAN Zhuo +4 位作者 WANG Peiyu PAN Qianghua LI Xiaoke GAN Xuehui CHEN Ge 《Journal of Donghua University(English Edition)》 2026年第1期118-130,共13页
In reliability analyses,the absence of a priori information on the most probable point of failure(MPP)may result in overlooking critical points,thereby leading to biased assessment outcomes.Moreover,second-order relia... In reliability analyses,the absence of a priori information on the most probable point of failure(MPP)may result in overlooking critical points,thereby leading to biased assessment outcomes.Moreover,second-order reliability methods exhibit limited accuracy in highly nonlinear scenarios.To overcome these challenges,a novel reliability analysis strategy based on a multimodal differential evolution algorithm and a hypersphere integration method is proposed.Initially,the penalty function method is employed to reformulate the MPP search problem as a conditionally constrained optimization task.Subsequently,a differential evolution algorithm incorporating a population delineation strategy is utilized to identify all MPPs.Finally,a paraboloid equation is constructed based on the curvature of the limit-state function at the MPPs,and the failure probability of the structure is calculated by using the hypersphere integration method.The localization effectiveness of the MPPs is compared through multiple numerical cases and two engineering examples,with accuracy comparisons of failure probabilities against the first-order reliability method(FORM)and the secondorder reliability method(SORM).The results indicate that the method effectively identifies existing MPPs and achieves higher solution precision. 展开更多
关键词 reliability analysis design point positioning differential evolution algorithm hypersphere integration
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基于TF-IDF算法的智能手部按摩仪设计研究
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作者 张琳 赵晶冉 林君晖 《工业设计》 2026年第1期142-145,共4页
文章旨在拓展亚健康青年群体的消费市场,满足现代青年群体对情绪价值的诉求。在消费者购买动机理论的指导下,文章针对新兴智能手部按摩产品开展设计方法方面的系统性研究。同时,借助TF-IDF算法与问卷调查法提取设计特征,通过排序转化构... 文章旨在拓展亚健康青年群体的消费市场,满足现代青年群体对情绪价值的诉求。在消费者购买动机理论的指导下,文章针对新兴智能手部按摩产品开展设计方法方面的系统性研究。同时,借助TF-IDF算法与问卷调查法提取设计特征,通过排序转化构建设计指标及原则,据此完成产品方案设计并引入灰色关联度分析法对原型进行优选。在案例研究中,所采用的TF-IDF算法可有效提炼出消费者的购买动机,将消费动机要素量化为数据形式。以期为智能手部按摩产品设计提取提供科学依据,使产品原型设计与青年群体消费心理相契合,亦为同类新兴智能康养按摩产品的创新研发提供理论参考与实践路径。 展开更多
关键词 工业设计 TF-IDF算法 智能手部按摩仪 灰色关联度分析法 消费者购买动机
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基于Kriging模型的瞬变工况下深沟球轴承结构优化设计
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作者 张泽琳 龙浩然 +2 位作者 王蕾 曹建华 夏绪辉 《机电工程》 北大核心 2026年第1期45-55,共11页
在瞬变工况下(如急加速),深沟球轴承会因惯性载荷增大和应力分布不均匀导致应力升高。针对这一问题,以深沟球轴承6208为研究对象,提出了一种融合瞬态动力学仿真、最佳填充空间试验设计(OPSD)、Kriging模型与多目标遗传算法(MOGA)的结构... 在瞬变工况下(如急加速),深沟球轴承会因惯性载荷增大和应力分布不均匀导致应力升高。针对这一问题,以深沟球轴承6208为研究对象,提出了一种融合瞬态动力学仿真、最佳填充空间试验设计(OPSD)、Kriging模型与多目标遗传算法(MOGA)的结构优化设计方法。首先,基于瞬态动力学分析建立了深沟球轴承多体动力学模型,通过节点动态等效应力分析揭示了钢球与内外圈接触区域的应力周期性波动规律,并设置了三种瞬变梯度工况,研究了加速度幅值对应力分布的影响,发现了最大应力随加速度增大而显著升高;然后,综合考虑了深沟球轴承在瞬变工况下各结构参数对应力的影响,选取了内、外圈沟道曲率半径系数和钢球直径作为设计变量,以深沟球轴承在瞬变工况下的最大等效应力和最大接触应力作为目标函数,结合最佳填充空间设计方法(OPSD),建立了设计变量与目标函数之间的Kriging响应面模型;最后,使用多目标遗传算法(MOGA)对深沟球轴承的设计参数进行了优化求解,得到了最优的设计参数组合,并对优化结果的可靠性进行了实验验证。研究结果表明:优化后的深沟球轴承最大等效应力从408.52 MPa降低至382.74 MPa,减少了6.31%;最大接触应力从451.61 MPa降低至415.05 MPa,减少了8.10%。该研究结果可为深沟球轴承的结构优化设计提供一种思路。 展开更多
关键词 滚动轴承 试验设计方法 KRIGING模型 瞬态动力学 最佳填充空间试验设计 多目标遗传算法 节点动态等效应力分析 多目标优化
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Multi-objective optimization of stamping forming process of head using Pareto-based genetic algorithm 被引量:11
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作者 周杰 卓芳 +1 位作者 黄磊 罗艳 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第9期3287-3295,共9页
To obtain the optimal process parameters of stamping forming, finite element analysis and optimization technique were integrated via transforming multi-objective issue into a single-objective issue. A Pareto-based gen... To obtain the optimal process parameters of stamping forming, finite element analysis and optimization technique were integrated via transforming multi-objective issue into a single-objective issue. A Pareto-based genetic algorithm was applied to optimizing the head stamping forming process. In the proposed optimal model, fracture, wrinkle and thickness varying are a function of several factors, such as fillet radius, draw-bead position, blank size and blank-holding force. Hence, it is necessary to investigate the relationship between the objective functions and the variables in order to make objective functions varying minimized simultaneously. Firstly, the central composite experimental(CCD) with four factors and five levels was applied, and the experimental data based on the central composite experimental were acquired. Then, the response surface model(RSM) was set up and the results of the analysis of variance(ANOVA) show that it is reliable to predict the fracture, wrinkle and thickness varying functions by the response surface model. Finally, a Pareto-based genetic algorithm was used to find out a set of Pareto front, which makes fracture, wrinkle and thickness varying minimized integrally. A head stamping case indicates that the present method has higher precision and practicability compared with the "trial and error" procedure. 展开更多
关键词 stamping forming HEADS finite element analysis central composite experimental design response surface methodology multi-objective genetic algorithm
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Fast and scalable routing protocols for data center networks
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作者 Mihailo Vesovic Aleksandra Smiljanic Dusan Kostic 《Digital Communications and Networks》 SCIE CSCD 2023年第6期1340-1350,共11页
Data center networks may comprise tens or hundreds of thousands of nodes,and,naturally,suffer from frequent software and hardware failures as well as link congestions.Packets are routed along the shortest paths with s... Data center networks may comprise tens or hundreds of thousands of nodes,and,naturally,suffer from frequent software and hardware failures as well as link congestions.Packets are routed along the shortest paths with sufficient resources to facilitate efficient network utilization and minimize delays.In such dynamic networks,links frequently fail or get congested,making the recalculation of the shortest paths a computationally intensive problem.Various routing protocols were proposed to overcome this problem by focusing on network utilization rather than speed.Surprisingly,the design of fast shortest-path algorithms for data centers was largely neglected,though they are universal components of routing protocols.Moreover,parallelization techniques were mostly deployed for random network topologies,and not for regular topologies that are often found in data centers.The aim of this paper is to improve scalability and reduce the time required for the shortest-path calculation in data center networks by parallelization on general-purpose hardware.We propose a novel algorithm that parallelizes edge relaxations as a faster and more scalable solution for popular data center topologies. 展开更多
关键词 Routing protocols Data center networks Parallel algorithms Distributed algorithms algorithm design and analysis Shortest-path problem SCALABILITY
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Application of Algorithm CARDBK in Document Clustering
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作者 ZHU Yehang ZHANG Mingjie SHI Feng 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2018年第6期514-524,共11页
In the K-means clustering algorithm, each data point is uniquely placed into one category. The clustering quality is heavily dependent on the initial cluster centroid. Different initializations can yield varied result... In the K-means clustering algorithm, each data point is uniquely placed into one category. The clustering quality is heavily dependent on the initial cluster centroid. Different initializations can yield varied results; local adjustment cannot save the clustering result from poor local optima. If there is an anomaly in a cluster, it will seriously affect the cluster mean value. The K-means clustering algorithm is only suitable for clusters with convex shapes. We therefore propose a novel clustering algorithm CARDBK—"centroid all rank distance(CARD)" which means that all centroids are sorted by distance value from one point and "BK" are the initials of "batch K-means"—in which one point not only modifies a cluster centroid nearest to this point but also modifies multiple clusters centroids adjacent to this point, and the degree of influence of a point on a cluster centroid depends on the distance value between this point and the other nearer cluster centroids. Experimental results showed that our CARDBK algorithm outperformed other algorithms when tested on a number of different data sets based on the following performance indexes: entropy, purity, F1 value, Rand index and normalized mutual information(NMI). Our algorithm manifested to be more stable, linearly scalable and faster. 展开更多
关键词 algorithm design and analysis CLUSTERING documentanalysis text processing
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Parallel Minimax Searching Algorithm for Extremum of Unimodal Unbounded Function
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作者 Boris S. Verkhovsky 《International Journal of Communications, Network and System Sciences》 2011年第9期549-561,共13页
In this paper we consider a parallel algorithm that detects the maximizer of unimodal function f(x) computable at every point on unbounded interval (0, ∞). The algorithm consists of two modes: scanning and detecting.... In this paper we consider a parallel algorithm that detects the maximizer of unimodal function f(x) computable at every point on unbounded interval (0, ∞). The algorithm consists of two modes: scanning and detecting. Search diagrams are introduced as a way to describe parallel searching algorithms on unbounded intervals. Dynamic programming equations, combined with a series of liner programming problems, describe relations between results for every pair of successive evaluations of function f in parallel. Properties of optimal search strategies are derived from these equations. The worst-case complexity analysis shows that, if the maximizer is located on a priori unknown interval (n-1], then it can be detected after cp(n)=「2log「p/2」+1(n+1)」-1 parallel evaluations of f(x), where p is the number of processors. 展开更多
关键词 Adversarial MINIMAX analysis design Parameters Dynamic Programming FUNCTION Evaluation Optimal algorithm PARALLEL algorithm System design Statistical Experiments Time Complexity Unbounded Search UNIMODAL FUNCTION
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A routing algorithm for FPGAs with time-multiplexed interconnects
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作者 Ruiqi Luo Xiaolei Chen Yajun Ha 《Journal of Semiconductors》 EI CAS CSCD 2020年第2期73-82,共10页
Previous studies show that interconnects occupy a large portion of the timing budget and area in FPGAs.In this work,we propose a time-multiplexing technique on FPGA interconnects.In order to fully exploit this interco... Previous studies show that interconnects occupy a large portion of the timing budget and area in FPGAs.In this work,we propose a time-multiplexing technique on FPGA interconnects.In order to fully exploit this interconnect architecture,we propose a time-multiplexed routing algorithm that can actively identify qualified nets and schedule them to multiplexable wires.We validate the algorithm by using the router to implement 20 benchmark circuits to time-multiplexed FPGAs.We achieve a 38%smaller minimum channel width and 3.8%smaller circuit critical path delay compared with the state-of-the-art architecture router when a wire can be time-multiplexed six times in a cycle. 展开更多
关键词 field programmable gate arrays digital integrated circuits routing algorithm design and analysis
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A Parallel Algorithm for the Spanning Forest Problem on Proper Circle Graphs
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作者 Hirotoshi Honma Yoko Nakajima Atsushi Sasaki 《Journal of Computer and Communications》 2017年第14期48-55,共8页
Given a simple graph G with n vertices, m edges and k connected components. The spanning forest problem is to find a spanning tree for each connected component of G. This problem has applications to the electrical pow... Given a simple graph G with n vertices, m edges and k connected components. The spanning forest problem is to find a spanning tree for each connected component of G. This problem has applications to the electrical power demand problem, computer network design, circuit analysis, etc. In this paper, we present an?time parallel algorithm with processors for constructing a spanning forest on proper circle graph G on EREW PRAM. 展开更多
关键词 design and analysis of Parallel algorithmS PROPER Circle GRAPHS SPANNING FOREST
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An Optimal Parallel Algorithm for Constructing a Spanning Tree on Proper Circle Trapezoid Graphs
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作者 Hirotoshi Honma Yoko Nakajima +1 位作者 Shino Nagasaki Atsushi Sasaki 《Journal of Applied Mathematics and Physics》 2018年第8期1649-1658,共10页
Given a simple graph G with n vertices and m edges, the spanning tree problem is to find a spanning tree for a given graph G. This problem has many applications, such as electric power systems, computer network design... Given a simple graph G with n vertices and m edges, the spanning tree problem is to find a spanning tree for a given graph G. This problem has many applications, such as electric power systems, computer network design and circuit analysis. For a simple graph, the spanning tree problem can be solved in O(log n) time with O(m+n) processors on the CRCW PRAM. In general, it is known that more efficient parallel algorithms can be developed by restricting classes of graphs. In this paper, we shall propose a parallel algorithm which runs O(log n) time with O(n/log n) processors on the EREW PRAM for constructing on proper circle trapezoid graphs. 展开更多
关键词 design and analysis of Parallel algorithms PROPER Circle TRAPEZOID GRAPHS SPANNING Tree
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