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Mathematics
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Advances in Network Modeling, Analysis and Optimization
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Advances in Network Modeling, Analysis and Optimization

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Network Science".

Deadline for manuscript submissions: closed (31 May 2023) | Viewed by 9866

Special Issue Editors

Dr. Yang Wang

E-Mail Website
Guest Editor
School of Arts and Sciences, La Salle University, Philadelphia, PA 19141, USA
Interests: network modeling; network optimization; optical networks; future internet
Dr. Maryam Jalalitabar

E-Mail Website
Guest Editor
Department of Computer Science, California State University, Northridge, CA 91330, USA
Interests: network function virtualization; software-defined networking; optical networks

Special Issue Information

Dear Colleagues,

The recent decade has witnessed revolutionary developments in various layers of networking. In this Special Issue, we aim to attract contributions reflecting novel applications and/or new developments of mathematical approaches (e.g., integer linear programming, combinatorial optimization approaches, queueing theory, graph theory, exact/approximation/online algorithms, decomposition-based approaches) in the arising network paradigms. We are particularly interested in studies concerning the modelling, analysis, and optimization of emerging network problems in the following (nonexhaustive) list of domains:

  1. Software-defined networks;
  2. Network virtualization;
  3. Network function virtualization;
  4. Edge/fog/cloud computing;
  5. Internet of Things (IoT);
  6. Optical networks;
  7. Social networks;
  8. Vehicular networks.

Dr. Yang Wang
Dr. Maryam Jalalitabar
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

  • network modelling
  • network analysis
  • network planning
  • network optimization
  • integer linear programming
  • approximation algorithm
  • online algorithm
  • decomposition algorithm
  • NP-Hard
  • SDN/NFV
  • network virtualization
  • optical networks
  • social networks
  • vehicular networks
  • Internet of Things (IoT)
  • fog computing
  • edge computing
  • cloud computing

Published Papers (3 papers)

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Research

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14 pages, 530 KiB  
Article
Kit of Uniformly Deployed Sets for p-Location Problems
by Jaroslav Janáček, Marek Kvet and Peter Czimmermann
Mathematics 2023, 11(11), 2418; https://doi.org/10.3390/math11112418 - 23 May 2023
Cited by 1 | Viewed by 712
Abstract
This paper deals with p-location problem solving processes based on a decomposition, which separates the creation of a uniformly deployed set of p-location problems from the solution of the p-location problem for that specific instance. The research presented in this [...] Read more.
This paper deals with p-location problem solving processes based on a decomposition, which separates the creation of a uniformly deployed set of p-location problems from the solution of the p-location problem for that specific instance. The research presented in this paper is focused on methods of construction of uniformly deployed sets of solutions and the examination of their impact on the efficiency of subsequent optimization algorithms. The approaches to the construction are used for the constitution of predetermined families of uniformly deployed sets of p-location problem solutions, which have standard sizes. We introduce two methods of uniformly deployed set construction: the first one is based on composition, followed by an enlargement process; and the second one makes use of voltage graphs. The construction approaches are completed by an algorithm, which adjusts the set of solutions to the sizes of a solved instance. The influence of a set construction approach on solving process efficiency is studied on real-world benchmarks, which include both the p-median objective function and the generalized disutility function. The solving process is performed alternatively using the swap or path-relinking based methods. Results of the computational study obtained by all combinations of the mentioned approaches are presented and evaluated in the concluding part of the paper to make the studied characteristics visible. Full article
(This article belongs to the Special Issue Advances in Network Modeling, Analysis and Optimization)
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15 pages, 3586 KiB  
Article
A Novel Context-Aware Reliable Routing Protocol and SVM Implementation in Vehicular Area Networks
by Manoj Sindhwani, Shippu Sachdeva, Akhil Gupta, Sudeep Tanwar, Fayez Alqahtani, Amr Tolba and Maria Simona Raboaca
Mathematics 2023, 11(3), 514; https://doi.org/10.3390/math11030514 - 18 Jan 2023
Cited by 6 | Viewed by 1027
Abstract
The Vehicular Ad-hoc Network (VANET) is an innovative technology that allows vehicles to connect with neighboring roadside structures to deliver intelligent transportation applications. To deliver safe communication among vehicles, a reliable routing approach is required. Due to the excessive mobility and frequent variation [...] Read more.
The Vehicular Ad-hoc Network (VANET) is an innovative technology that allows vehicles to connect with neighboring roadside structures to deliver intelligent transportation applications. To deliver safe communication among vehicles, a reliable routing approach is required. Due to the excessive mobility and frequent variation in network topology, establishing a reliable routing for VANETs takes a lot of work. In VANETs, transmission links are extremely susceptible to interruption; as a result, the routing efficiency of these constantly evolving networks requires special attention. To promote reliable routing in VANETs, we propose a novel context-aware reliable routing protocol that integrates k-means clustering and support vector machine (SVM) in this paper. The k-means clustering divides the routes into two clusters named GOOD and BAD. The cluster with high mean square error (MSE) is labelled as BAD, and the cluster with low MSE is labelled as GOOD. After training the routing data with SVM, the performance of each route from source to target is improved in terms of Packet Delivery Ratio (PDR), throughput, and End to End Delay (E2E). The proposed protocol will achieve improved routing efficiency with these changes. Full article
(This article belongs to the Special Issue Advances in Network Modeling, Analysis and Optimization)
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Review

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23 pages, 559 KiB  
Review
Recent Advances in Stochastic Gradient Descent in Deep Learning
by Yingjie Tian, Yuqi Zhang and Haibin Zhang
Mathematics 2023, 11(3), 682; https://doi.org/10.3390/math11030682 - 29 Jan 2023
Cited by 22 | Viewed by 7477
Abstract
In the age of artificial intelligence, the best approach to handling huge amounts of data is a tremendously motivating and hard problem. Among machine learning models, stochastic gradient descent (SGD) is not only simple but also very effective. This study provides a detailed [...] Read more.
In the age of artificial intelligence, the best approach to handling huge amounts of data is a tremendously motivating and hard problem. Among machine learning models, stochastic gradient descent (SGD) is not only simple but also very effective. This study provides a detailed analysis of contemporary state-of-the-art deep learning applications, such as natural language processing (NLP), visual data processing, and voice and audio processing. Following that, this study introduces several versions of SGD and its variant, which are already in the PyTorch optimizer, including SGD, Adagrad, adadelta, RMSprop, Adam, AdamW, and so on. Finally, we propose theoretical conditions under which these methods are applicable and discover that there is still a gap between theoretical conditions under which the algorithms converge and practical applications, and how to bridge this gap is a question for the future. Full article
(This article belongs to the Special Issue Advances in Network Modeling, Analysis and Optimization)
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