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Algorithms
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Graph Theoretic Methods in Scientific Computing & Industrial Applications
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Graph Theoretic Methods in Scientific Computing & Industrial Applications

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Combinatorial Optimization, Graph, and Network Algorithms".

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 5479

Special Issue Editors

Dr. Bogdan Zavalnij

E-Mail Website
Guest Editor
Head of Computer Department, Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, Budapest, Hungary
Interests: graph theory; combinatorial optimization; algorithms; high performacne computing
Dr. Miklós Krész

E-Mail Website
Guest Editor
Andrej Marušič Institute, University of Primorska, 6000 Koper, Slovenia
Interests: graph theory; data science
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Sándor Szabó

E-Mail Website
Guest Editor
Department of Applied Mathematics, University of Pécs, 48-as tér 1, 7622 Pécs, Hungary
Interests: graph theory; clique search problem

Special Issue Information

Dear Colleagues,

In the field of scientific computing, the concept of discrete models and methods has recently become a key approach. Graphs play a central role in both their modeling and efficient algorithmic arsenal. Intensive research has been pursued on graph algorithms, complex networks, large graphs and hard complexity class problems. The aim of the research community is to achieve a complex approach using graph-theoretical concepts that can integrate these topics. From the algorithmic perspective, there are huge differences in problem hardness. Some problems can be solved very quickly in polynomial time, such as finding the shortest path in a set of Google Maps directions. Other problems are much harder (i.e., NP-hard), such as clique search. Keen interest is currently directed towards the preconditioning and kernelization of these problems.

Currently, two main challenges are in the focus of future solutions. On one hand, there are those problems which inherently have the features of natural graph models. To mention a few examples, distances measured and clusters searched in network models for roads, social interactions or chemical interactions in complex systems as the human body. These require scalable methods for large graphs as well as the integration of intelligent technologies with graph-theoretic methods (e.g., machine learning). On the other hand, graphs can be considered a “modeling language” like numbers by representing hidden relationships that are far from obvious. In the case of these types of problems, the graph-building methodology is problem-specific. For analysis of the stock market, the market graph is built from the pairwise temporal correlation of stock price. Special graphs are constructed for proving mathematical conjectures (e.g., Keller’s conjecture). Auxiliary graphs can represent scheduling problems, protein docking sites and many more. Effective modeling can be far from trivial, and sporadic results have recently been achieved.

The objective of this Special Issue is to provide an opportunity for researchers focusing on both effective novel graph models for various applications fields as well as scalable efficient graph algorithms targeting the computation of solutions for complex graph-theoretic problems.

We welcome innovative contributions on all areas of graph theory and its applications. Topics include, but are not limited to:

  • Efficient graph algorithms—serial and parallel;
  • Heuristic graph algorithms for large graphs;
  • Exact algorithms for hard graph problems;
  • Preconditioning and kernelization of graph problems;
  • Machine learning aiding graph algorithms;
  • Modeling potential of graphs;
  • Application of graph algorithms;
  • Graph-theoretical concepts in scientific computing.

Dr. Bogdan Zavalnij
Dr. Miklós Krész
Prof. Dr. Sándor Szabó
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. Algorithms 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 1600 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 (5 papers)

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Research

11 pages, 4441 KiB  
Article
Exploratory Data Analysis and Searching Cliques in Graphs
by András Hubai, Sándor Szabó and Bogdán Zaválnij
Algorithms 2024, 17(3), 112; https://doi.org/10.3390/a17030112 - 07 Mar 2024
Viewed by 739
Abstract
The principal component analysis is a well-known and widely used technique to determine the essential dimension of a data set. Broadly speaking, it aims to find a low-dimensional linear manifold that retains a large part of the information contained in the original data [...] Read more.
The principal component analysis is a well-known and widely used technique to determine the essential dimension of a data set. Broadly speaking, it aims to find a low-dimensional linear manifold that retains a large part of the information contained in the original data set. It may be the case that one cannot approximate the entirety of the original data set using a single low-dimensional linear manifold even though large subsets of it are amenable to such approximations. For these cases we raise the related but different challenge (problem) of locating subsets of a high dimensional data set that are approximately 1-dimensional. Naturally, we are interested in the largest of such subsets. We propose a method for finding these 1-dimensional manifolds by finding cliques in a purpose-built auxiliary graph. Full article
(This article belongs to the Special Issue Graph Theoretic Methods in Scientific Computing & Industrial Applications)
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11 pages, 248 KiB  
Article
Binary Numeration System with Alternating Signed Digits and Its Graph Theoretical Relationship
by Péter Hajnal
Algorithms 2024, 17(2), 55; https://doi.org/10.3390/a17020055 - 25 Jan 2024
Viewed by 1027
Abstract
The binary number system is the basic number representation in computing. We can encode natural numbers with finite 0-1 sequences. The representation of natural numbers is based on this system. However, this poses problems and is technically not perfect. Several attempts have been [...] Read more.
The binary number system is the basic number representation in computing. We can encode natural numbers with finite 0-1 sequences. The representation of natural numbers is based on this system. However, this poses problems and is technically not perfect. Several attempts have been made to handle integers (signed numbers). We mention only two: the balanced triple number system and the number system with base −2. Our paper introduces new possibilities. We also shed light on the graph theoretical background of the new number systems. Full article
(This article belongs to the Special Issue Graph Theoretic Methods in Scientific Computing & Industrial Applications)
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18 pages, 375 KiB  
Article
A Generalized Framework for the Estimation of Edge Infection Probabilities
by András Bóta and Lauren Gardner
Algorithms 2023, 16(8), 390; https://doi.org/10.3390/a16080390 - 16 Aug 2023
Viewed by 798
Abstract
Modeling the spread of infections in networks is a well-studied and important field of research. Most infection and diffusion models require a real value or probability at the edges of the network as an input, but this is rarely available in real-life applications. [...] Read more.
Modeling the spread of infections in networks is a well-studied and important field of research. Most infection and diffusion models require a real value or probability at the edges of the network as an input, but this is rarely available in real-life applications. The Generalized Inverse Infection Model (GIIM) has previously been used in real-world applications to solve this problem. However, these applications were limited to the specifics of the corresponding case studies, and the theoretical properties, as well as the wider applicability of the model, are yet to be investigated. Here, we show that the general model works with the most widely used infection models and is able to handle an arbitrary number of observations on such processes. We evaluate the accuracy and speed of the GIIM on a large variety of realistic infection scenarios. Full article
(This article belongs to the Special Issue Graph Theoretic Methods in Scientific Computing & Industrial Applications)
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15 pages, 485 KiB  
Article
Minimizing Interference-to-Signal Ratios in Multi-Cell Telecommunication Networks
by Péter L. Erdős and Tamás Róbert Mezei
Algorithms 2023, 16(7), 341; https://doi.org/10.3390/a16070341 - 17 Jul 2023
Viewed by 798
Abstract
In contemporary wireless communication networks, base stations are organized into coordinated clusters (called cells) to jointly serve the users. However, such fixed systems are plagued by the so-called cell-edge problem: near the boundaries, the interference between neighboring clusters can result in very [...] Read more.
In contemporary wireless communication networks, base stations are organized into coordinated clusters (called cells) to jointly serve the users. However, such fixed systems are plagued by the so-called cell-edge problem: near the boundaries, the interference between neighboring clusters can result in very poor interference-to-signal power ratios. To achieve a high-quality service, it is an important objective to minimize the sum of these ratios over the cells. The most common approach to solving this minimization problem is arguably the spectral clustering method. In this paper, we propose a new clustering approach, which is deterministic and computationally much less demanding than current methods. Simulating on synthetic instances indicates that our methods typically provide higher quality solutions than earlier methods. Full article
(This article belongs to the Special Issue Graph Theoretic Methods in Scientific Computing & Industrial Applications)
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19 pages, 402 KiB  
Article
Adding a Tail in Classes of Perfect Graphs
by Anna Mpanti, Stavros D. Nikolopoulos and Leonidas Palios
Algorithms 2023, 16(6), 289; https://doi.org/10.3390/a16060289 - 03 Jun 2023
Viewed by 983
Abstract
Consider a graph G which belongs to a graph class C. We are interested in connecting a node w∉V(G) to G by a single edge uw where u∈V(G); we call [...] Read more.
Consider a graph G which belongs to a graph class C. We are interested in connecting a node w∉V(G) to G by a single edge uw where u∈V(G); we call such an edge a tail. As the graph resulting from G after the addition of the tail, denoted G+uw, need not belong to the class C, we want to compute the number of non-edges of G in a minimum C-completion of G+uw, i.e., the minimum number of non-edges (excluding the tail uw) to be added to G+uw so that the resulting graph belongs to C. In this paper, we study this problem for the classes of split, quasi-threshold, threshold and P4-sparse graphs and we present linear-time algorithms by exploiting the structure of split graphs and the tree representation of quasi-threshold, threshold and P4-sparse graphs. Full article
(This article belongs to the Special Issue Graph Theoretic Methods in Scientific Computing & Industrial Applications)
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