NM-DPoS: 基于牛顿冷却定律和修正沙普利值的DPoS优化共识算法

廖国琼; 谢玉芳; 邓小鸿; 雷银香; 丁皓; 罗丹

doi:10.11999/JEIT250069

NM-DPoS: 基于牛顿冷却定律和修正沙普利值的DPoS优化共识算法

doi: 10.11999/JEIT250069

廖国琼^{1, 2},
谢玉芳^{1, 3, ,},
邓小鸿⁴,
雷银香^{1, 5},
丁皓¹,
罗丹¹

1.
江西财经大学信息管理与数学学院南昌 330013
2.
江西旅游商贸职业学院南昌 330100
3.
江西科技师范大学教育技术与信息中心南昌 330038
4.
赣南科技学院信息工程学院赣州 341000
5.
江西中医药大学计算机学院南昌 330004

基金项目: 国家自然科学基金(62272207)，江西省自然科学基金(20224ACB202009)

详细信息

作者简介:
廖国琼：男，博士生导师，教授，研究方向为区块链、数据库

谢玉芳：女，博士生，研究方向为区块链

邓小鸿：男，博士，教授，研究方向为网络信息安全、区块链

雷银香：女，博士生，研究方向为区块链、数据挖掘

丁皓：男，博士生，研究方向为区块链

罗丹：女，博士生，研究方向为数智文旅、区块链

通讯作者:
谢玉芳　1020130978@jxstnu.edu.cn

中图分类号: TN915; TP309
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- 被引次数: 0
出版历程
- 收稿日期: 2025-02-12
- 修回日期: 2025-05-13
- 网络出版日期: 2025-05-24

NM-DPoS: Optimized DPoS Consensus Algorithm Based on Newton’s Cooling Law and Modified Shapley Value

LIAO Guoqiong^{1, 2},
XIE Yufang^{1, 3
, ,},
DENG Xiaohong⁴,
LEI Yinxiang^{1, 5},
DING Hao¹,
LUO Dan¹

1.
School of Information Management and Mathematics, Jiangxi University of Finance and Economics, Nanchang 330013, China
2.
Jiangxi Tourism and Commerce Vocational College, Nanchang 330100, China
3.
Centre for Educational and Information Technology, Jiangxi Science and Technology Normal University, Nanchang 330038, China
4.
School of Information Engineering, Gannan University of Science and Technology, Ganzhou 341000, China
5.
School of Information Engineering, Jiangxi University of Chinese Medicine, Nanchang 330004, China

Funds: The National Natural Science Foundation of China (62272207), The Natural Science Foundation of Jiangxi Province (20224ACB202009)

摘要

摘要: 针对委托权益证明共识算法(DPoS)中，寡头节点造成的中心化现象、节点投票积极性不高和未投票导致的资源浪费问题，该文提出一种基于牛顿冷却定律和修正沙普利值的DPoS优化共识算法(NM-DPoS)。首先，设计基于牛顿冷却定律的衰减机制使节点的投票权重随时间逐渐衰减，但可根据投票表现获得额外的热补偿，同时，增加代理节点在连任时所需的委托权重，以降低寡头节点带来的中心化风险；其次，构建投票节点和代理节点的利益共同体，使得为代理节点投票的节点也能获得出块收益，并提出基于修正沙普利值的利益分配机制，根据投票节点的贡献度来进行合理的分配，提升节点的投票积极性；最后，设计动态分区投票机制，将节点投票区段分为正常区段和代投区段，并根据投票情况动态调整两者的区间比例，提升了整体的投票效率和避免投票资源的浪费。仿真实验表明，与DPoS算法相比，NM-DPoS的平均时延降低了32.9%，平均吞吐量提高了18.7%，且节点的投票速率提升了约36%。与其他DPoS优化算法相比，所提算法也具有明显的性能优势，能够确保区块链网络在大规模节点环境下的公平性和去中心化特性。
- 区块链 /
- 共识算法 /
- 委托权益证明 /
- 牛顿冷却定律 /
- 沙普利值
Abstract: Objective Blockchain systems rely on consensus algorithms to maintain data consistency, ensure tamper resistance, and enhance network security and fault tolerance. Delegated Proof of Stake (DPoS), a widely adopted consensus mechanism, improves block confirmation rates and reduces computational demands by electing a limited number of agent nodes through voting. Despite its advantages—namely high throughput and low resource consumption—DPoS remains vulnerable to centralization risks due to the dominance of oligarchic nodes. Furthermore, the absence of incentives for voters discourages participation and results in underutilization of network resources. To address these limitations, this study proposes an optimized DPoS consensus algorithm based on Newton’s Cooling Law and modified Shapley (NM-DPoS) value theory. The proposed algorithm enhances voting fairness, mitigates centralization risks, and improves node participation, providing a theoretical basis for the broader application of blockchain technology in practical systems. Methods Firstly, a weight attenuation mechanism based on Newton’s Cooling Law is developed. In this scheme, the voting weight of nodes decays over time, while nodes demonstrating better performance receive additional weight compensation. To curb the dominance of oligarchic nodes and reduce centralization risk, the delegated weight required for agent node re-election is progressively increased.Secondly, a shared-interest community between voting nodes and agent nodes is established. Under this framework, voting nodes receive a portion of the block rewards. A reward distribution scheme based on a modified Shapley value is introduced to allocate incentives proportionally, according to each node’s contribution, thereby encouraging broader participation.Finally, a dynamic partition voting mechanism is proposed. The voting period is divided into normal and proxy voting phases, with the ratio between these segments adjusted dynamically in response to network latency and the proportion of participating nodes. This design improves voting efficiency and reduces resource waste. Results and Discussions As shown in (Fig. 6), with an increasing number of nodes, all comparison algorithms exhibit declining throughput and increasing delay. However, NM-DPoS maintains a more stable performance. Compared with standard DPoS, NM-DPoS reduces average delay by 32.9% and increases average throughput by 18.7%, demonstrating superior adaptability to dynamic network conditions. (Fig. 7) illustrates that the attenuation mechanism in NM-DPoS effectively constrains high-weight nodes, thereby enhancing the competitiveness of low-weight nodes. Therefore, block generation becomes more evenly distributed across nodes compared with other algorithms, indicating that NM-DPoS reduces the risk of node oligopoly and improves system stability. As seen in (Fig. 8), NM-DPoS substantially increases node participation in voting, with the voting rate improving by approximately 36% relative to DPoS. This improvement results from incorporating voting efficiency as a performance metric, which incentivizes nodes to vote actively in pursuit of greater rewards. (Fig. 9) shows that NM-DPoS penalizes malicious nodes by deducting their deposits and disqualifying them from re-election. This mechanism facilitates the rapid exclusion of malicious actors and thereby enhances system security more effectively than other optimized algorithms. Conclusions This study proposes an optimized consensus algorithm, NM-DPoS, based on Newton’s Cooling Law and modified Shapley values. A weight attenuation mechanism is introduced to mitigate the centralization risk posed by oligarchic nodes. To enhance voting participation, nodes receive rewards proportional to their contributions, allocated through a modified Shapley value-based distribution scheme. In addition, NM-DPoS incorporates a proxy voting phase to improve voting efficiency and overall participation rates. Despite these improvements, the current scheme does not provide fine-grained handling of malicious nodes. Future work will focus on classifying malicious behaviors and refining penalty mechanisms to ensure fairer and more targeted enforcement, thereby improving the algorithm’s robustness and applicability across different blockchain environments.
- Blockchain /
- Consensus algorithm /
- Delegated Proof of Stake (DPoS) /
- Newton’s cooling law /
- Shapley value

HTML全文

图 1 NM-DPoS共识过程

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图 2 权重补偿

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图 3 投票区段变化

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图 4 节点代投

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图 5 节点排列情况

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图 6 吞吐量和时延对比

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图 7 区块生产占比

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图 8 投票速率对比

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图 9 恶意节点数量变化

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表 1 变量含义

变量	含义
$ {\phi _j}(N,v) $	边际贡献值
$ n $	联盟N中节点的总数量
$ T $	在N中除j以外的所有节点组成的任意子集
$ v(T \cup \{ j\} ) $	j加入联盟T后的总收益
$ v(T\} ) $	联盟T中所有节点的总收益

下载: 导出CSV

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