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European Journal of Operational Research 2025年第1期326卷 13-27页

作者： Creemers, Stefan Voie du Roman Pays 34 Louvain-la-NeuveB-1348 Belgium

To find one of the M target entries in an unstructured database that has N entries, Grover's algorithm performs [Formula presented][Formula presented] iterations. In each iteration, a function is called that evaluates whether an entry is a target entry. Compared to a classical procedure, that requires [Formula presented] evaluations, Grover's algorithm achieves a quadratic speedup. This quadratic speedup, combined with its general applicability as a search algorithm, have made Grover's algorithms one of the most important (quantum) algorithms available today. A study to improve its runtime is more than justified. For this purpose, we investigate two speedup strategies: (1) reducing the number of iterations that are performed in each run of Grover's algorithm and (2) partitioning the database. For each of these strategies, we not only execute Grover's algorithm in parallel, but also explore the possibility to execute Grover's algorithm in series on a single Quantum Processing Unit (QPU) as well as on multiple QPUs. For each combination of execution mode (serial, parallel, and serial/parallel) and speedup strategy, we show how to obtain optimal policies using closed-form expressions and a gradient-descent procedure. For a single QPU we obtain a speedup factor of 1.1382 when compared to a textbook implementation of Grover's algorithm. If multiple QPUs are at our disposal, we obtain a speedup factor of at most 1.1382Q, where Q denotes the number of QPUs. In addition, we show that the dominant policies that minimize the expected number of Grover iterations also minimize the expected number of iterations that are performed per qubit. © 2025 Elsevier B.V.

关键词： consensus algorithm

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Practical Byzantine improved algorithm based on node-independent validation

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COMPUTER NETWORKS 2025年 265卷

作者： Li, Anqi Zhang, Quan Xu, Xin Yao, Yingbiao Hangzhou Dianzi Univ Commun Engn Hangzhou 310000 Zhejiang Peoples R China

The PBFT consensus algorithm solves the Byzantine node tolerance problem of Raft and Paxos consensus algorithms, but the three-stage confirmation leads to its poor scalability and high communication latency. In response to above problems, this paper proposes an improved PBFT algorithm based on node-independent validation, briefly as V-PBFT. V-PBFT divides nodes into a double layer structure with multiple leaders, and sets up global validation nodes, intra-group followers, suspicious nodes and malicious nodes. Firstly, V-PBFT adopts the PBFT protocol to reach consensus among leaders. Validation nodes guarantee the consistency of the state of leaders. Then, leaders broadcast Intra-consensus messages to intra-group followers. Secondly, validation nodes broadcast Verify messages to all nodes except malicious nodes and leaders. The messages from the leader and validation nodes are mutually verified, enabling followers to judge the correctness of client requests. Finally, the credit value is set for followers to reduce the probability on malicious view-changes. Experimental results show that V-PBFT reduces the communication complexity of PBFT from the quadratic level to the linear level and thus its communication latency is significantly reduced.

关键词： Blockchain Byzantine fault tolerance consensus algorithm Credit value election Node validation

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BDLS as a Blockchain Finality Gadget: Improving Byzantine Fault Tolerance in Hyperledger Fabric

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IEEE ACCESS 2024年 12卷 154600-154613页

作者： Salih, Ahmed Al Wang, Yongge Univ North Carolina Charlotte Dept Software & Informat Syst SIS Charlotte NC 28223 USA Coll Comp & Informat Charlotte NC 28223 USA

Decentralized systems are integral to various sectors, including public and private organizations. At the core of these systems is the dissemination protocol. Hyperledger Fabric, a prominent production-ready distribution network system, allows for a pluggable consensus protocol, though it has historically lacked detailed technical guidance for implementing such modules. Initially, Fabric employed Kafka and later switched to Raft, both of which are Crash Fault Tolerant (CFT) protocols and do not support Byzantine fault tolerance (BFT). Hyperledger Fabric recently introduced a new BFT solution called SmartBFT in its 3.0 release. However, SmartBFT, based on the Practical Byzantine Fault Tolerance (PBFT) protocol family, suffers from high message complexity, explicitly referring to the total number of messages exchanged during protocol execution, which scales poorly as the network grows. This complexity significantly affects network efficiency, particularly in large-scale implementations across industries such as healthcare, finance, and education. Communication overhead increases substantially, which encompasses the number of messages and the time and resources required for message transmission and processing. Our research shows that the message complexity of SmartBFT grows quadratically with the number of orderer nodes, leading to significant communication overhead. Conversely, our proposed implementation of our Byzantine Fault Tolerant (BFT) protocol is based on the original Dwork, Lynch, and Stockmeyer (DLS) protocol. Our adaptation is the Blockchain version of DLS (BDLS), which maintains linear message complexity, making it more scalable and efficient for large networks. This stark contrast highlights BDLS's superior scalability and efficiency. BDLS maintains a consistent performance advantage. BDLS throughput analysis of Fabric 3.0 shows a significant performance drop for SmartBFT, which achieves only 40 % and 20 % of Raft's TPS in LAN and WAN environments, respec

关键词： Fabrics Protocols Distributed ledger Fault tolerance consensus algorithm Complexity theory Throughput consensus protocol Blockchains Blockchain Byzantine fault tolerance (BFT) consensus distributed ledger technology

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Enhancing Privacy in Microgrid Operations: A State Decomposition Approach for consensus-Based Distributed Economic Dispatch over Directed Networks

Enhancing Privacy in Microgrid Operations: A State Decomposi...

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2024 China Automation Congress, CAC 2024

作者： Xu, Keng Xiang, Hanbing Yan, Gangfeng Kuai, Jiating Zhejiang University Hangzhou China Zhejiang Institute of Communications Co. Ltd. Hangzhou China

ISBN: (纸本)9798350368604

The dual objectives of privacy protection and optimization scheduling are of paramount importance in economic dispatch for smart microgrids. This study presents a privacy-preserving consensus algorithm that employs state decomposition to tackle the privacy leakage challenges associated with distributed economic dispatch in smart microgrids. By decomposing state variables into internal and external sub-states, the algorithm selectively transmits partial data, effectively preventing information leakage. Compared with traditional methods such as noise injection and encryption, the proposed algorithm offers lower computational complexity while maintaining rapid convergence. Privacy analysis demonstrates the robustness of the algorithm against both internal and external eavesdroppers, ensuring the security of sensitive information. The results from numerical simulations affirm the algorithm’s efficacy. This approach is applicable to ED problems in smart microgrids with privacy protection requirements, providing a novel solution for secure and efficient microgrid operation. © 2024 IEEE.

关键词： consensus algorithm

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DISTRIBUTED EXTENDED STOCHASTIC GRADIENT algorithm FOR JOINT IDENTIFICATION OF SYSTEM PARAMETERS AND NOISE MODEL PARAMETERS

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SIAM Journal on Control and Optimization 2025年第1期63卷 650-675页

作者： Gan, Die Yan, Ren Chen, Shuning Liu, Zhixin College of Artificial Intelligence Nankai University Tianjin China Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100190 China

In this paper, we study the distributed identification problem of dynamic systems described by stochastic regression models with colored noise. To deal with challenges brought by the colored noise, we provide estimates for the unknown noise over a previous time period, and incorporate them with observed signals to construct extended regression vectors. Based on this, we develop a distributed extended stochastic gradient algorithm to estimate unknown parameter matrices by integrating the diffusion strategy of extended regression vectors with the consensus strategy of neighbors' estimates. We introduce cooperative nonpersistent excitation conditions to reflect the temporal and spatial union information condition, under which the almost sure convergence of the proposed distributed algorithm is established. Our results are obtained without assuming the independence, stationarity or persistent excitation conditions for the regressors and the Gaussian property for the system noises. Finally, numerical results are provided to verify the effectiveness of our proposed algorithm. © by SIAM.

关键词： consensus algorithm

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Decision-making algorithm based on the energy of interval-valued hesitant fuzzy soft sets

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Neural Computing and Applications 2025年 1-21页

作者： Stojanović, Nenad Laković, Maja Djurović, Ljubica Faculty of Science University of Kragujevac 34000 Radoja Domanovića 12 Kragujevac Serbia

Interval-valued hesitant fuzzy soft sets, a powerful tool for data modeling, have been the focus of numerous studies. In addition to their various applications, examining the properties and characteristics of these structures from a theoretical mathematical perspective enables more efficient utilization in real-world problems. The primary objective of this research is to define a numerical characteristic of an interval-valued hesitant fuzzy soft set, analogous to the energy of a graph and the energy of a fuzzy soft set. The motivation for introducing this numerical characteristic lies in its potential to develop a decision-making algorithm that outperforms existing approaches addressing the same problem. The energy of a graph, as well as the energy of a fuzzy soft set, is defined as a norm function obtained by summing the singular values of the corresponding representation matrix. In optimization problems, this sum of singular values is known as the nuclear norm, which serves as the basis for introducing the notion of energy in interval-valued hesitant fuzzy soft sets. The results of the proposed algorithm are compared in this paper with those of various existing algorithms designed to solve the same problem. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2025.

关键词： consensus algorithm

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Memetic algorithm for Maximizing K-coverage and K-Connectivity in Wireless Sensor Network

Informatica (Slovenia)

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Informatica (Slovenia) 2025年第1期49卷 7-18页

作者： Thi, Hanh Nguyen Van Duc, Cuong Duc, Chinh Tran Minh, Hieu Ha Van, Son Nguyen Van, Quan La Faculty of Interdisciplinary Digital Technology PHENIKAA University Yen Nghia Ha Dong Hanoi12116 Viet Nam Hanoi University of Science and Technology Hanoi Viet Nam Faculty of Computer Science PHENIKAA University Yen Nghia Ha Dong Hanoi12116 Viet Nam

The rapid growth of IoT has enabled diverse applications using Wireless Sensor Networks across various fields. A significant challenge in Wireless Sensor Networks is the efficient deployment of sensors to ensure coverage and connectivity. Effective coverage allows continuous target tracking and data collection, while connectivity ensures data transmission to the base station. In this paper, we address the challenge of maximizing the number of targets satisfying K-coverage and K-connectivity, where each target is tracked by K sensors and has K transmission paths to the base station. We propose a two-phase methodology to tackle this challenge. The first phase enhances the Greedy algorithm to solve the K-coverage problem. The second phase addresses the K-connectivity problem using Memetic algorithms augmented by an efficient local search mechanism called PMA. We evaluate the algorithm on various datasets and compare it with baseline methods, including Greedy and Prim-based with the withdrawal strategy (PWS). Our results show that the proposed PMA with a robust local search outperforms alternative algorithms, with improvements exceeding 10% to 15% compared to the baseline methods. Additionally, we validate the performance of the proposed method using a real-world dataset and outline plans for further enhancements in the near future. © 2025 Slovene Society Informatika. All rights reserved.

关键词： consensus algorithm

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Practical Parallel algorithms for Non-Monotone Submodular Maximization

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Journal of Artificial Intelligence Research 2025年 82卷 39-75页

作者： Cui, Shuang Han, Kai Tang, Jing Li, Xueying Zhiyuli, Aakas Li, Hanxiao School of Computer Science and Technology Soochow University Jiangsu Suzhou China The Hong Kong University of Science and Technology China Alibaba Group Zhejiang Hangzhou China Qingdao University of Science and Technology Shandong Qingdao China

Submodular maximization has found extensive applications in various domains within the field of artificial intelligence, including but not limited to machine learning, computer vision, and natural language processing. With the increasing size of datasets in these domains, there is a pressing need to develop efficient and parallelizable algorithms for submodular maximization. One measure of the parallelizability of a submodular maximization algorithm is its adaptive complexity, which indicates the number of sequential rounds where a polynomial number of queries to the objective function can be executed in parallel. In this paper, we study the problem of non-monotone submodular maximization subject to a knapsack constraint, and propose a low-adaptivity algorithm achieving an (1/8 − ϵ)approximation with practical Õ(n) query complexity. Moreover, we also propose the first algorithm with both provable approximation ratio and sublinear adaptive complexity for the problem of non-monotone submodular maximization subject to a k-system constraint. As a by-product, we show that our two algorithms can also be applied to the special case of submodular maximization subject to a cardinality constraint, and achieve performance bounds comparable with those of state-of-the-art algorithms. Finally, the effectiveness of our algorithms is demonstrated by extensive experiments on real-world applications. ©2025 The Authors.

关键词： consensus algorithm

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Blockchain-Based User Authentication and Data-Sharing Framework for Healthcare Industries

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2024年第4期11卷 3623-3638页

作者： Soni, Preeti Islam, S. K. Hafizul Pal, Arup Kumar Mishra, Nimish Samanta, Debabrata Natl Inst Technol Hamirpur Dept Comp Sci & Engn Hamirpur 177005 India Indian Inst Informat Technol Kalyani Dept Comp Sci & Engn Kalyani 741235 West Bengal India Indian Inst Technol Dhanbad Indian Sch Mines Dept Comp Sci & Engn Jharkhand 826004 India Rochester Inst Technol Dept Comp & Informat Technol Prishtina 10000 Kosovo

In this paper, we developed a Blockchain-based User Authentication Data-Sharing (BC-UADS) framework. In BC-UADS, several hospital servers form a consortium blockchain network to maintain the transparency, immutability, and authenticity of the patient's Electronic Healthcare (Record EHR) medical data. The BC-UADS framework allows doctors to share or retrieve a patient's EHR metadata from the blockchain network. Since, the metadata is stored on a blockchain platform, it is more secure and trusted for real-time applications to utilize the medical data. The data-sharing protocol of the BC-UADS framework is implemented based on Proof-of-Reputation consensus algorithm in a blockchain network. The BC-UADS framework is analyzed in the AVISPA (Automated Validation of Internet Security Protocols and Applications) tool, demonstrating that it is secure against active and passive attacks. Besides, the BC-UADS framework is provably secure in the random oracle model based on the hardness assumption of Elliptic Curve-based Computational Diffie-Hellman (ECCDH) problem. The mutual authentication property of the BC-UADS framework is analyzed in the BAN (Burrows-Abadi-Needham) logic model. We have computed the communication, execution, and storage costs of the BC-UADS framework in different security levels: 80-bit, 112-bit, 128-bit, 192-bit, and 256-bit using PBC library. The proposed BC-UADS framework is compared with the state-of-the-art schemes.

关键词： Blockchains Hospitals Authentication Servers consensus algorithm Elliptic curves Costs blockchain healthcare provable security proof-of-reputation

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CG-PBFT: an efficient PBFT algorithm based on credit grouping

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JOURNAL OF CLOUD COMPUTING-ADVANCES SYSTEMS AND APPLICATIONS 2024年第1期13卷 1-20页

作者： Liu, Juan Deng, Xiaohong Li, Wangchun Li, Kangting JiangXi Univ Sci & Technol Sch Informat Engn Ganzhou 341000 Peoples R China Gannan Univ Sci & Technol Sch Elect & Informat Engn Ganzhou 341000 Peoples R China Key Lab Cloud Comp & Big Data Ganzhou 341000 Peoples R China

Because of its excellent properties of fault tolerance, efficiency and availability, the practical Byzantine fault tolerance (PBFT) algorithm has become the mainstream consensus algorithm in blockchain. However, current PBFT algorithms have problems such as inadequate security of primary node selection, high communication overhead and network delay in the process of consensus. To address these problems, we design a novel efficient Byzantine fault tolerance algorithm based on credit grouping, called CG-PBFT. First, we propose a new credit evaluation model to obtain nodes' credit values and introduce an optimized three-way quick sorting algorithm to divide nodes into the master-node group, the consensus-node group and the observation-node group, which have different privileges. The nodes in the observation-node group are restricted from participating in consensus, which reduces the communication overhead and improves consensus efficiency. Second, we propose an optimized selection method for the primary node based on a voting mechanism whereby the consensus-node group and observation-node group vote to produce the primary node, which reduces the probability of malicious nodes acting as the primary node and improves the security of primary node selection. Finally, the identity conversion mechanism between node groups is designed, and the actual behavior of nodes within different groups is given credit rewards or punishment, so as to keep an incentive for nodes to participate in appropriate system behavior and improve the working enthusiasm of nodes. The experimental simulation results show that compared with existing PBFT algorithms, the CG-PBFT algorithm improves the average throughput by 51.3% and reduces the average delay by 64.5%;it greatly improves the operating efficiency of the system and can be more suitable for application in the consortium blockchain scenarios.

关键词： Blockchain consensus algorithm Byzantine fault tolerance Credit grouping Quick sorting

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