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Mathematics
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Mathematical Modeling for Parallel and Distributed Processing, 2nd Edition
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Mathematical Modeling for Parallel and Distributed Processing, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 28 February 2025 | Viewed by 6782

Special Issue Editors

Dr. Tian-Yi Li

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Guest Editor
Department of Computer Science, Aalborg University, 9220 Aalborg, Denmark
Interests: spatiotemporal database; distributed optimization; big graph data mining
Special Issues, Collections and Topics in MDPI journals
Dr. Yushuai Li

E-Mail Website
Guest Editor
Department of Computer Science, Aalborg University, 9220 Aalborg, Denmark
Interests: distributed optimization; machine learning; digital twin; energy internet; autonomous driving
Special Issues, Collections and Topics in MDPI journals
Dr. Peiyuan Guan

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Guest Editor
Department of Informatics, University of Oslo, 0316 Oslo, Norway
Interests: edge computing; real-time systems; task scheduling; deep learning; reinforcement learning
Special Issues, Collections and Topics in MDPI journals
Dr. Lingxiao Yang

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Guest Editor
School of Artificial Intelligence, Anhui University, Hefei 230093, China
Interests: deep reinforcement learning; energy management; distributed optimization
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Lu Chen

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Guest Editor
College of Computer Science, Zhejiang University, Hangzhou 310027, China
Interests: database; big data management; AI interaction with dB technology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Parallel and distributed processing have become increasingly essential for solving computationally intensive tasks. With the exponential growth of data and the increasing availability of CPU cores, efficient parallel and distributed processing solutions have become more desirable. However, despite decades of development, some fundamental challenges still exist, such as the distributed knowledge discovery of large-scale data, peer-to-peer energy trading under complex system environments, the improvement of the services in intelligent transportation systems, parallel training in deep learning and intelligent network management and task scheduling. Mathematical models can help address these challenges through resource utilization optimization, data mining and analytics, energy consumption minimization, and the reduction of communication overheads. By incorporating powerful mathematical models into parallel and distributed processing, we can achieve better performances, optimize computation and communication between nodes, and overcome the fundamental challenges that exist in this field.

The main objective of this Special Issue is to showcase innovative research that combines parallel and distributed computing with powerful and smart mathematical methods. We welcome submissions that present the latest developments in distributed optimization, machine learning-based distributed network management and orchestration, algorithm design, and mathematical modeling, as well as their applications in big data processing, data usability, energy, transportation, aerospace, and 5G/6G. By highlighting the latest advances in these fields, we aim to generate new ideas and foster collaborations that can address the current challenges and drive further progress in parallel and distributed computing.

Dr. Tian-Yi Li
Dr. Yushuai Li
Dr. Peiyuan Guan
Dr. Lingxiao Yang
Prof. Dr. Lu Chen
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • algebraic digital techniques
  • distributed computing
  • parallel processing
  • algorithm design
  • mathematical modeling
  • optimization

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Related Special Issue

Published Papers (6 papers)

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Research

20 pages, 2770 KiB  
Article
Fast Frequency Control Strategy Based on Worst-Case Network Attack Perception
by Wentao Xu, Zhenghang Song and Peiyuan Guan
Mathematics 2025, 13(1), 132; https://doi.org/10.3390/math13010132 - 31 Dec 2024
Viewed by 489
Abstract
A fast frequency control (FFC) strategy using the proximal policy optimization based on worst-case network attack perception (worst-case PPO) algorithm is proposed to address the complexity of fast frequency control in power systems and the risks posed by network attacks. This strategy focuses [...] Read more.
A fast frequency control (FFC) strategy using the proximal policy optimization based on worst-case network attack perception (worst-case PPO) algorithm is proposed to address the complexity of fast frequency control in power systems and the risks posed by network attacks. This strategy focuses on frequency stability in power systems with a high penetration of renewable energy, and utilizes a reinforcement learning agent to intelligently adjust the power setpoint of voltage source converters (VSCs), ensuring that both the frequency and the rate of change of the frequency remain within permissible limits. Considering the potential for network attacks, this strategy adopts the robust worst-case PPO algorithm, which ensures system stability even under the worst-case attack scenarios. The experimental results demonstrate that the proposed strategy effectively prevents frequency degradation under various disturbances, exhibiting a stronger disturbance resistance and robustness compared to traditional reinforcement learning methods. Furthermore, the strategy is easy to implement, highly adaptable, and suitable for the complex and dynamic operational environment of power systems, providing strong support for the secure and stable operation of smart grids. Full article
(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing, 2nd Edition)
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23 pages, 613 KiB  
Article
Comprehensive Evaluation Method of Privacy-Preserving Record Linkage Technology Based on the Modified Criteria Importance Through Intercriteria Correlation Method
by Shumin Han, Yue Li, Derong Shen and Chuang Wang
Mathematics 2024, 12(22), 3476; https://doi.org/10.3390/math12223476 - 7 Nov 2024
Viewed by 824
Abstract
The era of big data has brought rapid growth and widespread application of data, but the imperfections in the existing data integration system have become obstacles to its high-quality development. The conflict between data security and shared utilization is significant, with traditional data [...] Read more.
The era of big data has brought rapid growth and widespread application of data, but the imperfections in the existing data integration system have become obstacles to its high-quality development. The conflict between data security and shared utilization is significant, with traditional data integration methods risking data leakage and privacy breaches. The proposed Privacy-Preserving Record Linkage (PPRL) technology, has effectively resolved this contradiction, enabling efficient and secure data sharing. Currently, many solutions have been developed for PPRL issues, but existing assessments of PPRL methods mainly focus on single indicators. There is a scarcity of comprehensive evaluation and comparison frameworks that consider multiple indicators of PPRL(such as linkage quality, computational efficiency, and security), making it challenging to achieve a comprehensive and objective assessment. Therefore, it has become an urgent issue for us to conduct a multi-indicator comprehensive evaluation of different PPRL methods to explore the optimal approach. This article proposes the use of an modified CRITIC method to comprehensively evaluate PPRL methods, aiming to select the optimal PPRL method in terms of linkage quality, computational efficiency, and security. The research results indicate that the improved CRITIC method based on mathematical statistics can achieve weight allocation more objectively and quantify the allocation process effectively. This approach exhibits exceptional objectivity and broad applicability in assessing various PPRL methods, thereby providing robust scientific support for the optimization of PPRL techniques. Full article
(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing, 2nd Edition)
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19 pages, 3569 KiB  
Article
Enhanced Multi-Party Privacy-Preserving Record Linkage Using Trusted Execution Environments
by Shumin Han, Kuixing Shen, Derong Shen and Chuang Wang
Mathematics 2024, 12(15), 2337; https://doi.org/10.3390/math12152337 - 26 Jul 2024
Viewed by 864
Abstract
With the world’s data volume growing exponentially, it becomes critical to link it and make decisions. Privacy-preserving record linkage (PPRL) aims to identify all the record information corresponding to the same entity from multiple data sources, without disclosing sensitive information. Previous works on [...] Read more.
With the world’s data volume growing exponentially, it becomes critical to link it and make decisions. Privacy-preserving record linkage (PPRL) aims to identify all the record information corresponding to the same entity from multiple data sources, without disclosing sensitive information. Previous works on multi-party PPRL methods typically adopt homomorphic encryption technology due to its ability to perform computations on encrypted data without needing to decrypt it first, thus maintaining data confidentiality. However, these methods have notable shortcomings, such as the risk of collusion among participants leading to the potential disclosure of private keys, high computational costs, and decreased efficiency. The advent of trusted execution environments (TEEs) offers a solution by protecting computations involving private data through hardware isolation, thereby eliminating reliance on trusted third parties, preventing malicious collusion, and improving efficiency. Nevertheless, TEEs are vulnerable to side-channel attacks. In this work, we propose an enhanced PPRL method based on TEE technology. Our methodology involves processing plaintext data within a TEE using the inner product mask technique, which effectively obfuscates the data, making it impervious to side-channel attacks. The experimental results demonstrate that our approach not only significantly improves resistance to side-channel attacks but also enhances efficiency, showing better performance and privacy preservation compared to existing methods. This work provides a robust solution to the challenges faced by current PPRL methods and sets the stage for future research aimed at further enhancing scalability and security. Full article
(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing, 2nd Edition)
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26 pages, 2261 KiB  
Article
Learning from Feature and Global Topologies: Adaptive Multi-View Parallel Graph Contrastive Learning
by Yumeng Song, Xiaohua Li, Fangfang Li and Ge Yu
Mathematics 2024, 12(14), 2277; https://doi.org/10.3390/math12142277 - 21 Jul 2024
Viewed by 1669
Abstract
To address the limitations of existing graph contrastive learning methods, which fail to adaptively integrate feature and topological information and struggle to efficiently capture multi-hop information, we propose an adaptive multi-view parallel graph contrastive learning framework (AMPGCL). It is an unsupervised graph representation [...] Read more.
To address the limitations of existing graph contrastive learning methods, which fail to adaptively integrate feature and topological information and struggle to efficiently capture multi-hop information, we propose an adaptive multi-view parallel graph contrastive learning framework (AMPGCL). It is an unsupervised graph representation learning method designed to generate task-agnostic node embeddings. AMPGCL constructs and encodes feature and topological views to mine feature and global topological information. To encode global topological information, we introduce an H-Transformer to decouple multi-hop neighbor aggregations, capturing global topology from node subgraphs. AMPGCL learns embedding consistency among feature, topology, and original graph encodings through a multi-view contrastive loss, generating semantically rich embeddings while avoiding information redundancy. Experiments on nine real datasets demonstrate that AMPGCL consistently outperforms thirteen state-of-the-art graph representation learning models in classification accuracy, whether in homophilous or non-homophilous graphs. Full article
(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing, 2nd Edition)
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26 pages, 7621 KiB  
Article
A Parallel Multi-Party Privacy-Preserving Record Linkage Method Based on a Consortium Blockchain
by Shumin Han, Zikang Wang, Dengrong Shen and Chuang Wang
Mathematics 2024, 12(12), 1854; https://doi.org/10.3390/math12121854 - 14 Jun 2024
Cited by 1 | Viewed by 918
Abstract
Privacy-preserving record linkage (PPRL) is the process of linking records from various data sources, ensuring that matching records for the same entity are shared among parties while not disclosing other sensitive data. However, most existing PPRL approaches currently rely on third parties for [...] Read more.
Privacy-preserving record linkage (PPRL) is the process of linking records from various data sources, ensuring that matching records for the same entity are shared among parties while not disclosing other sensitive data. However, most existing PPRL approaches currently rely on third parties for linking, posing risks of malicious tampering and privacy breaches, making it difficult to ensure the security of the linkage. Therefore, we propose a parallel multi-party PPRL method based on consortium blockchain technology which can effectively address the issue of semi-trusted third-party validation, auditing all parties involved in the PPRL process for potential malicious tampering or attacks. To improve the efficiency and security of consensus within a consortium blockchain, we propose a practical Byzantine fault tolerance consensus algorithm based on matching efficiency. Additionally, we have incorporated homomorphic encryption into Bloom filter encoding to enhance its security. To optimize computational efficiency, we have adopted the MapReduce model for parallel encryption and utilized a binary storage tree as the data structure for similarity computation. The experimental results show that our method can effectively ensure data security while also exhibiting relatively high linkage quality and scalability. Full article
(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing, 2nd Edition)
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20 pages, 5253 KiB  
Article
A Multi-Party Privacy-Preserving Record Linkage Method Based on Secondary Encoding
by Shumin Han, Yizi Wang, Derong Shen and Chuang Wang
Mathematics 2024, 12(12), 1800; https://doi.org/10.3390/math12121800 - 9 Jun 2024
Viewed by 1338
Abstract
With the advent of the big data era, data security and sharing have become the core elements of new-era data processing. Privacy-preserving record linkage (PPRL), as a method capable of accurately and securely matching and sharing the same entity across multiple data sources, [...] Read more.
With the advent of the big data era, data security and sharing have become the core elements of new-era data processing. Privacy-preserving record linkage (PPRL), as a method capable of accurately and securely matching and sharing the same entity across multiple data sources, is receiving increasing attention. Among the existing research methods, although PPRL methods based on Bloom Filter encoding excel in computational efficiency, they are susceptible to privacy attacks, and the security risks they face cannot be ignored. To balance the contradiction between security and computational efficiency, we propose a multi-party PPRL method based on secondary encoding. This method, based on Bloom Filter encoding, generates secondary encoding according to well-designed encoding rules and utilizes the proposed linking rules for secure matching. Owing to its excellent encoding and linking rules, this method successfully addresses the balance between security and computational efficiency. The experimental results clearly show that, in comparison to the original Bloom Filter encoding, this method has nearly equivalent computational efficiency and linkage quality. The proposed rules can effectively prevent the re-identification problem in Bloom Filter encoding (proven). Compared to existing privacy-preserving record linkage methods, this method shows higher security, making it more suitable for various practical application scenarios. The introduction of this method is of great significance for promoting the widespread application of privacy-preserving record linkage technology. Full article
(This article belongs to the Special Issue Mathematical Modeling for Parallel and Distributed Processing, 2nd Edition)
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