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Mathematics
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Graph Theory and Network Theory
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Graph Theory and Network Theory

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

Deadline for manuscript submissions: 30 April 2025 | Viewed by 2000

Special Issue Editor

Dr. Majid Forghani-elahabad

E-Mail Website
Guest Editor
Center of Mathematics, Computing, and Cognition—Federal University of ABC, Santo André 09210-580, SP, Brazil
Interests: network flows; reliability; optimization; optical networks

Special Issue Information

Dear Colleague,

This Special Issue is dedicated to the application of graph theory in network optimization and network reliability problems. We invite submissions focusing on network optimization problems, such as minimal path, shortest path, minimum cost path, max flow, assignment, transportation problems, as well as related topics. Additionally, we welcome papers addressing network reliability problems, including both binary state flow networks and multistate flow networks, and employing exact and approximation approaches such as simulation techniques, upper and lower bounds methods, and minimal path- and minimal cut-based algorithms. We strongly encourage submissions with real-world applications and those with a theoretical focus that have potential practical implications.

Dr. Majid Forghani-elahabad
Guest Editor

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 optimization
  • network reliability
  • binary state flow networks
  • multistate flow networks
  • exact and approximation approaches, and algorithms.

Published Papers (2 papers)

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Research

15 pages, 464 KiB  
Article
Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints
by Majid Forghani-elahabad and Omar Mutab Alsalami
Mathematics 2023, 11(24), 4889; https://doi.org/10.3390/math11244889 - 06 Dec 2023
Viewed by 659
Abstract
The quickest path problem in multistate flow networks, which is also known as the quickest path reliability problem (QPRP), aims at calculating the probability of successfully sending a minimum of d flow units/data/commodity from a source node to a destination node via one [...] Read more.
The quickest path problem in multistate flow networks, which is also known as the quickest path reliability problem (QPRP), aims at calculating the probability of successfully sending a minimum of d flow units/data/commodity from a source node to a destination node via one minimal path (MP) within a specified time frame of T units. Several exact and approximative algorithms have been proposed in the literature to address this problem. Most of the exact algorithms in the literature need prior knowledge of all of the network’s minimal paths (MPs), which is considered a weak point. In addition to the time, the budget is always limited in real-world systems, making it an essential consideration in the analysis of systems’ performance. Hence, this study considers the QPRP under cost constraints and provides an efficient approach based on a node–child matrix to address the problem without knowing the MPs. We show the correctness of the algorithm, compute the complexity results, illustrate it through a benchmark example, and describe our extensive experimental results on one thousand randomly generated test problems and well-established benchmarks to showcase its practical superiority over the available algorithms in the literature. Full article
(This article belongs to the Special Issue Graph Theory and Network Theory)
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16 pages, 1904 KiB  
Article
Robust Design Problem for Multi-Source Multi-Sink Flow Networks Based on Genetic Algorithm Approach
by Sahbi Boubaker, Noha Hamdy Radwan, Moatamad Refaat Hassan, Faisal S. Alsubaei, Ahmed Younes and Hameda A. Sennary
Mathematics 2023, 11(18), 3902; https://doi.org/10.3390/math11183902 - 13 Sep 2023
Viewed by 826
Abstract
Robust design problems in flow networks involve determining the optimal capacity assignments that enable the network to operate effectively even in the case of events’ occurrence such as arcs or nodes’ failures. Multi-source multi-sink flow networks (MMSFNs) are frequent in many real-life systems [...] Read more.
Robust design problems in flow networks involve determining the optimal capacity assignments that enable the network to operate effectively even in the case of events’ occurrence such as arcs or nodes’ failures. Multi-source multi-sink flow networks (MMSFNs) are frequent in many real-life systems such as computer and telecommunication, logistics and supply-chain, and urban traffic. Although numerous studies on the design of MMSFNs have been conducted, the robust design problem for multi-source multi-sink stochastic-flow networks (MMSFNs) remains unexplored. To contribute to this field, this study addresses the robust design problem for MMSFNs using an approach of two steps. First, the problem is mathematically formulated as an optimization problem and second, a sub-optimal solution is proposed based on a genetic algorithm (GA) involving two components. The first component, an outer genetic algorithm, is employed to search the optimal capacity assigned to the network components with minimum sum. The second component, an inner genetic algorithm, is used to find the optimal flow vectors that maximize the system’s reliability. Through extensive experimentation on three different networks with different topologies, the proposed solution has been found to be efficient. Full article
(This article belongs to the Special Issue Graph Theory and Network Theory)
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