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作者： Liang, Jing School of Finance and Mathematics Huainan Normal University Anhui Huainan232001 China

Mathematics studies the objective law of reality, analyzes and solves the practical problems by describing the known problems. With the continuous integration of information technology and computer industry, big data analysis technology is becoming more and more important. The application of mathematical algorithm in data analysis can simplify the processing of complex problems. So this article studies the mathematical algorithm deeply. This article applies experimental and comparative methods. Experimental data show that mathematical algorithms can enable learners to form a keen sense of numbers and cultivate their logical thinking, with a correlation of 0.51 and 0.47, respectively. This can play a certain role in big data analysis. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： consensus algorithm

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Unplugging Dijkstra’s algorithm as a Mechanical Device 7th

Unplugging Dijkstra’s Algorithm as a Mechanical Device

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7th International Conference on Creative Mathematical Sciences Communication, CMSC 2024

作者： Jacob, Riko Silvestri, Francesco IT University of Copenhagen Copenhagen Denmark University of Padua Padua Italy

ISBN: (纸本)9783031732560

Graphs are a fundamental concept in computer science, effectively modeling diverse scenarios such as social networks, protein interactions, and mobility. Dijkstra’s algorithm is crucial for computing single-source shortest path in graphs and is a key component of graph processing. This paper presents an educational activity designed to "unplug" graphs and Dijkstra’s algorithm, making these topics accessible to a broad audience. The activity utilizes a physical graph with chains as edges and key rings with retractable badge holders as nodes. By pulling two nodes of this graph apart, it is possible to find a shortest path between these nodes. This can be used to visualize how Dijkstra’s algorithm works, including how the graph models the world. It invites for discussing how much more efficient this is compared to enumerating all paths, and what additional insights computer scientists had to achieve impressive speedups over plain Dijkstra, allowing for route planning to be perceived as a solved problem, where we use the packaged solution without further thought. We discuss the implementation of this activity in public outreach events, such as Culture Nights and primary school classrooms. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： consensus algorithm

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A Simple Control algorithm to Reduce the DC Current Level in a CSI-UPQC

A Simple Control Algorithm to Reduce the DC Current Level in...

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International Conference of the TC Electrimacs Committee, ELECTRIMACS 2024

作者： Melín C., P.E. Baier F., C.R. Espinosa N., E.E. Reyes M., M.E. Hernandez C., F.A. Espinoza C., J.R. Universidad del Bío-Bío Concepción Chile Universidad de Talca Curicó Chile Universidad Catolica de la Santisima Concepción Concepción Chile Universidad de Concepción Concepción Chile

ISBN: (纸本)9783031739200

This work deals with a simple algorithm to define the dc current reference of a CSI-UPQC aimed to reduce its losses. The proposal uses the mathematical model of the CSI-UPQC to demonstrate the relationship between the dc current level and the modulation amplitude of the series stage. With this concept, a straightforward algorithm is proposed to set the dc current level to keep the modulation index of the series stage in a preset range, allowing to reduce of the dc current level compared with the use of a fixed dc current level and, therefore, reducing the losses in the power valves and dc inductor. The mathematical analysis illustrates the proposal, and simulated results corroborate it. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： consensus algorithm

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Fast, Fair and Truthful Distributed Stable Matching for Common Preferences 28

Fast, Fair and Truthful Distributed Stable Matching for Comm...

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28th International Conference on Principles of Distributed Systems, OPODIS 2024

作者： Hirvonen, Juho Ranjbaran, Sara Helsinki Institute for Information Technology HIIT Finland Department of Computer Science Aalto University Espoo Finland

ISBN: (纸本)9783959773607

Stable matching is a fundamental problem studied both in economics and computer science. The task is to find a matching between two sides of agents that have preferences over who they want to be matched with. A matching is stable if no pair of agents prefer each other over their current matches. The deferred acceptance algorithm of Gale and Shapley solves this problem in polynomial time. Further, it is a mechanism: the proposing side in the algorithm is always incentivised to report their preferences truthfully. The deferred acceptance algorithm has a natural interpretation as a distributed algorithm (and thus a distributed mechanism). However, the algorithm is slow in the worst case and it is known that the stable matching problem cannot be solved efficiently in the distributed setting. In this work we study a natural special case of the stable matching problem where all agents on one of the two sides share common preferences. We show that in this case the deferred acceptance algorithm does yield a fast and truthful distributed mechanism for finding a stable matching. We show how algorithms for sampling random colorings can be used to break ties fairly and extend the results to fractional stable matching. © Juho Hirvonen and Sara Ranjbaran.

关键词： consensus algorithm

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A Study on Accelerating Average consensus algorithms Using Delayed Feedback

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2023年第1期10卷 157-168页

作者： Moradian, Hossein Kia, Solmaz S. Univ Calif Irvine Dept Mech & Aerosp Engn Irvine CA 92697 USA

This article studies accelerating a Laplacian-based dynamic average consensus algorithm by splitting the conventional delay-free disagreement feedback into a weighted summation of current and outdated terms. When determining the weighted sum, there is a range of time delay that results in a higher convergence rate for the algorithm. For such weights, using the Lambert W function, we obtain the rate-increasing range of the time delay, obtain the maximum reachable rate, and characterize the value of the corresponding maximizer delay. We also study the effect of using the outdated feedback on the control effort of the agents. We show that only for some specific affine combination of the immediate and outdated feedback, the control effort of the agents does not go beyond that of the delay-free algorithm. In addition, we demonstrate that using outdated feedback does not increase the steady-state tracking error of the average consensus algorithm. Finally, we determine the optimum combination of the current and the outdated feedback weights to achieve the maximum increase in the rate of convergence without increasing the control effort of the agents. We demonstrate our results through a numerical example.

关键词： Convergence Delays Heuristic algorithms consensus algorithm Laplace equations Delay effects Network topology Accelerated algorithms average consensus distributed systems

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Tight Bounds on the Convergence Rate of Generalized Ratio consensus algorithms

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第4期67卷 1669-1684页

作者： Gerencser, Balazs Gerencser, Laszlo Eotvos Lorand Res Network ELKH Alfred Renyi Inst Math H-1053 Budapest Hungary Eotvos Lorand Univ Dept Probabil & Stat H-1117 Budapest Hungary Eotvos Lorand Res Network ELKH Inst Comp Sci & Control SZTAKI H-1111 Budapest Hungary

The problems discussed in this article are motivated by general ratio consensus algorithms, introduced by Kempe et al. in 2003 in a simple form as the push-sum algorithm, later extended by Benezit et al. in 2010 under the name weighted gossip algorithm. We consider a communication protocol described by a strictly stationary, ergodic, sequentially primitive sequence of nonnegative matrices, applied iteratively to a pair of fixed initial vectors, the components of which are called values and weights defined at the nodes of a network. The subject of ratio consensus problems is to study the asymptotic properties of ratios of values and weights at each node, expecting convergence to the same limit for all nodes. The main results of this article provide upper bounds for the rate of the almost sure exponential convergence in terms of the spectral gap associated with the given sequence of random matrices. It will be shown that these upper bounds are sharp. Our results complement previous results of Picci and Taylor in 2013 and Iutzeler et al. in 2013.

关键词： Convergence Upper bound consensus algorithm Symmetric matrices Heuristic algorithms Technological innovation Protocols Asynchronous communication convergence communication networks distributed computing estimation iterative algorithms multiagent systems random processes spectral gap

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Three-Dimensional Tradeoffs for consensus algorithms: A Review

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IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT 2022年第2期19卷 1216-1228页

作者： Li, Linhui Shi, Peichang Fu, Xiang Chen, Peng Zhong, Tao Kong, Jinzhu Natl Univ Def Technol Coll Comp Sci Natl Key Lab Parallel & Distributed Proc Changsha 410073 Peoples R China Natl Univ Def Technol Coll Comp Sci Key Lab Software Engn Complex Syst Changsha 410073 Peoples R China Zhejiang Lab Hangzhou 311100 Peoples R China Kylin Software Co Ltd Changsha 410073 Peoples R China

Blockchain has been applied in many fields to solve the problems of trust, security, efficiency benefiting from its tamper-proof and traceability of data. However, it is still necessary to consider the technical constraints that limit the large-scale application of blockchain: scalability, security, and decentralization cannot be achieved altogether. consensus algorithm is the core of blockchain, which determines the performance of blockchain system to a certain extent. The existing reviews or surveys mainly focus on processes of consensus algorithms, but fall short in covering the current trends and scenarios, thereby lacking intrinsic understanding of their design philosophy. In this paper, we propose a multi-dimensional tradeoff model and unearth various indicators of different dimensions to guide the construction of consensus algorithms. To summarize the existing efforts, we compare and analyze various classical consensus algorithms, and focus on the design principles of these algorithms under the multi-dimensional tradeoff model. According to different requirements, each algorithm has different tradeoffs. Furthermore, we provide different solutions for blockchain in different dimensions. Finally, we summarize the development trend of consensus design and the key technology prospects of blockchain. This is, to the best of our knowledge, the first survey that accomplishes such goals.

关键词： Blockchains Security consensus algorithm Scalability Throughput Bitcoin Technological innovation Scalability decentralization security consensus

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Term Dictionary Automatic Extraction algorithm based on BiLSTM 1

Term Dictionary Automatic Extraction Algorithm based on BiLS...

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1st International Conference on Intelligent Systems and Computational Networks, ICISCN 2025

作者： Liu, Fangting Bohai University College of Foreign Languages Jinzhou China

ISBN: (纸本)9798331529246

With the increasing importance of machine translation research in the era of artificial intelligence, which are widely used in translation practice, contrastive analysis, language learning and other fields. As a basic resource, terminology dictionary plays an important role in cross-language natural language processing. To solve the problems in the field of cross-language natural language processing, this paper takes parallel corpus as the basis, studies the automatic extraction algorithm of term dictionary based on BiLSTM, combines BiLSTM, HMM, Viterbi and T-test and other methods to build a mathematical model of automatic extraction of term dictionary based on parallel corpus. Solve key problems such as sentence alignment, part-of-speech tagging and Chinese word segmentation. Through simulation experiments, the BiLSTM algorithm model in this paper is compared with RNN, CRF, LSTM and other network algorithm models, and the superiority of BiLSTM algorithm model is verified. © 2025 IEEE.

关键词： consensus algorithm

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Hash & Adjust: Competitive Demand-Aware Consistent Hashing 28

Hash & Adjust: Competitive Demand-Aware Consistent Hashing

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28th International Conference on Principles of Distributed Systems, OPODIS 2024

作者： Pourdamghani, Arash Avin, Chen Sama, Robert Shiran, Maryam Schmid, Stefan TU Berlin Germany Ben-Gurion University of the Negev Beersheba Israel University of Vienna Austria Fraunhofer SIT Berlin Germany

ISBN: (纸本)9783959773607

Distributed systems often serve dynamic workloads and resource demands evolve over time. Such a temporal behavior stands in contrast to the static and demand-oblivious nature of most data structures used by these systems. In this paper, we are particularly interested in consistent hashing, a fundamental building block in many large distributed systems. Our work is motivated by the hypothesis that a more adaptive approach to consistent hashing can leverage structure in the demand, and hence improve storage utilization and reduce access time. We initiate the study of demand-aware consistent hashing. Our main contribution is H&A, a constant-competitive online algorithm (i.e., it comes with provable performance guarantees over time). H&A is demand-aware and optimizes its internal structure to enable faster access times, while offering a high utilization of storage. We further evaluate H&A empirically. © Arash Pourdamghani, Chen Avin, Robert Sama, Maryam Shiran, and Stefan Schmid.

关键词： consensus algorithm

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Engineering Fully Dynamic Exact ∆-Orientation algorithms

Engineering Fully Dynamic Exact ∆-Orientation Algorithms

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2025 SIAM Symposium on algorithm Engineering and Experiments, ALENEX 2025

作者： Großmann, Ernestine Reinstädtler, Henrik Schulz, Christian Walliser, Fabian Heidelberg University Germany

ISBN: (纸本)9798331311995

A (fully) dynamic graph algorithm is a data structure that supports edge insertions, edge deletions, and answers specific queries pertinent to the problem at hand. In this work, we address the fully dynamic edge orientation problem, also known as the fully dynamic ∆-orientation problem. The objective is to maintain an orientation of the edges in an undirected graph such that the out-degree of any vertex remains low. When edges are inserted or deleted, it may be necessary to reorient some edges to prevent vertices from having excessively high out-degrees. In this paper, we introduce the first algorithm that maintains an optimal edge orientation during both insertions and deletions. In experiments comparing with recent nearly exact algorithms, we achieve a 32% lower running time. The update time of our algorithm is up to 6 orders of magnitude faster than static exact algorithms. Copyright © 2025 by SIAM.

关键词： consensus algorithm

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