Symmetry in Graph Algorithms and Graph Theory III

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: 31 July 2024 | Viewed by 1681

Special Issue Editor

Department of Computer Science, Université de Sherbrooke, Sherbrooke, QC, Canada
Interests: algorithms; computational biology; graph theory; parameterized complexity; approximation algorithms
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Following the success of the second Special Issue of Symmetry entitled “Graph Algorithms and Graph Theory II”, it is my pleasure to be the Guest Editor for a third Special Issue.

Graphs have applications in numerous areas of computer science, including machine learning, computational biology, social network analysis, and many other areas, which all require fast algorithms for various optimization problems. Recent advancements in graph theory have shown that most graphs exhibit structural properties or symmetry that can be leveraged for the development of efficient algorithms. To cite a few examples, minor theory has paved the way for countless results in parameterized complexity, and several regularity lemmata have stimulated several new ideas in approximation algorithms. Moreover, these results only represent a fraction of the algorithmic applications of structural graph theory that have emerged over the last few decades. This demonstrates that expanding our fundamental knowledge of graphs, whether it be graphs in general or specific classes, is necessary in order to improve the state of the art in algorithms and complexity.

This Special Issue aims to improve our understanding of the interplay between algorithms, structure, and symmetry in graphs. The goal is to explore new directions in designing graph algorithms and to establish new foundations in structural graph theory.

The scope of the Special Issue includes, but is not limited to:

  • The design and analysis of graph algorithms, as well as parallel, randomized, parameterized, distributed, and other types of algorithms;
  • Structural graph theory with immediate or potential applications in algorithms and complexity analysis.

Dr. Manuel Lafond
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. Symmetry is an international peer-reviewed open access monthly 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 2400 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.

Published Papers (2 papers)

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Research

17 pages, 6547 KiB  
Article
Virtual Coordinate System Based on a Circulant Topology for Routing in Networks-On-Chip
Symmetry 2024, 16(1), 127; https://doi.org/10.3390/sym16010127 - 21 Jan 2024
Viewed by 623
Abstract
In this work, the circulant topology as an alternative to 2D mesh in networks-on-chip is considered. A virtual coordinate system for numbering nodes in the circulant topology is proposed, and the principle of greedy promotion is formulated. The rules for constructing the shortest [...] Read more.
In this work, the circulant topology as an alternative to 2D mesh in networks-on-chip is considered. A virtual coordinate system for numbering nodes in the circulant topology is proposed, and the principle of greedy promotion is formulated. The rules for constructing the shortest routes between the two nodes based on coordinates are formulated. A technique for calculating optimal network configurations is described. Dense states of the network when all neighborhoods of the central node are filled with nodes and the network has the smallest diameter are defined. It is shown that with an equal number of nodes, the diameter of the circulant is two times smaller than the diameter of the 2D mesh. This is due to the large number of symmetries for the circulant, which leave the set of nodes unchanged. A comparison of communication stability in both topologies in the conditions of failure of network nodes is made, the network behavior under load and failures is modeled, and the advantages of the circulant topology are presented. Full article
(This article belongs to the Special Issue Symmetry in Graph Algorithms and Graph Theory III)
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28 pages, 9032 KiB  
Article
Modeling and Simulation of Physical Systems Formed by Bond Graphs and Multibond Graphs
Symmetry 2023, 15(12), 2170; https://doi.org/10.3390/sym15122170 - 06 Dec 2023
Viewed by 633
Abstract
Current physical systems are built in more that one coordinate: for example, electrical power systems, aeronautical systems and robotic systems can be modeled in multibond graphs (MBG). However, in these systems, some elements use only one axis or [...] Read more.
Current physical systems are built in more that one coordinate: for example, electrical power systems, aeronautical systems and robotic systems can be modeled in multibond graphs (MBG). However, in these systems, some elements use only one axis or dimension—for example, actuators and controllers—which can be modeled in bond graphs (BG). Therefore, in this paper, modeling of systems in multibond graphs and bond graphs (MBG-BG) is presented. Likewise, the junction structure of systems represented by (MBG-BG) is introduced. From this structure, mathematical modeling in the state space is presented. Likewise, modeling of systems on a platform (MBG-BG) can be seen as symmetric to the mathematical model that represents these systems. Finally, a synchronous generator modeled by (MBG-BG) as a case study is developed, and simulation results using 20-Sim software are shown. Furthermore, an electrical power system connected to the power supply of a DC motor as another case study is explained. Full article
(This article belongs to the Special Issue Symmetry in Graph Algorithms and Graph Theory III)
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