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Algorithms
Special Issues
Graph Theory and Algorithmic Applications: Theoretical Developments
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Graph Theory and Algorithmic Applications: Theoretical Developments

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 March 2025) | Viewed by 2776

Special Issue Editor

Dr. Paul Hunter

E-Mail Website
Guest Editor
School of Computer Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia
Interests: formal verification; graph theory; algorithms; education

Special Issue Information

Dear Colleagues,

The algorithmic application of graph structure theory is not at all unexpected: as we learn more about what makes a graph "complex", we learn more about the computational complexity of graph-based problems. This connection is perhaps best exemplified by the seminal Graph Minors Project of Robertson and Seymour. Graph parameters, such as pathwidth and treewidth, developed in the Graph Minors project have provided efficient algorithms for many problems pertaining to large classes of graphs.

The algorithmic success of structure-based parameters such as treewidth encouraged many further advancements in this area, including the following:

  • The development of algorithmic meta-theorems inspired by Courcelle to uniformly extend these efficient algorithms to large classes of problems.
  • An increased interest in multi-dimensional complexity analysis with the development of parameterized algorithms.
  • The development of similar, algorithmically beneficial graph parameters such as rank-width, twin-width, and DAG-width.

In this Special Issue, we invite contributions that explore the algorithmic benefits arising from developments in graph theory. Topics of interest include, but are not limited to, the following:

  • Exact, parameterized, or classical algorithms for graph problems.
  • Novel, algorithmically interesting, graph parameters.
  • Graph-based algorithmic meta-theorems.
  • Any of the above topics applied to other classes of graphs such as random graphs, directed graphs, and/or hypergraphs.

Dr. Paul Hunter
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. 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.

Keywords

  • graph theory
  • algorithms
  • graph parameters
  • treewidth
  • pathwidth
  • parameterized algorithms
  • meta-theorems
  • directed graphs
  • hypergraphs

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

19 pages, 364 KiB  
Article
A New Algorithm for Computing the Distance and the Diameter in Circulant Graphs
by Laila Loudiki and Mustapha Kchikech
Algorithms 2025, 18(5), 261; https://doi.org/10.3390/a18050261 - 1 May 2025
Viewed by 156
Abstract
In the present study, we focus on circulant graphs, Cn(S), with set of vertices {0,1,…,n−1} and in which two distinct vertices i and j are adjacent if and [...] Read more.
In the present study, we focus on circulant graphs, Cn(S), with set of vertices {0,1,…,n−1} and in which two distinct vertices i and j are adjacent if and only if |i−j|n∈S, where S is a generating set. Despite their regularity, there are currently no established formulas to accurately determine the distance and the diameter of circulant graphs. In light of this context, we present in this paper a novel approach, which relies on a simple algorithm, capable of yielding formulas for the distance and the diameter of circulant graphs without implementing any graph. Full article
(This article belongs to the Special Issue Graph Theory and Algorithmic Applications: Theoretical Developments)
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14 pages, 252 KiB  
Article
Impossibility Results for Byzantine-Tolerant State Observation, Synchronization, and Graph Computation Problems
by Ajay D. Kshemkalyani and Anshuman Misra
Algorithms 2025, 18(1), 26; https://doi.org/10.3390/a18010026 - 5 Jan 2025
Cited by 1 | Viewed by 711
Abstract
This paper considers the solvability of several fundamental problems in asynchronous message-passing distributed systems in the presence of Byzantine processes using distributed algorithms. These problems are the following: mutual exclusion, global snapshot recording, termination detection, deadlock detection, predicate detection, causal ordering, spanning tree [...] Read more.
This paper considers the solvability of several fundamental problems in asynchronous message-passing distributed systems in the presence of Byzantine processes using distributed algorithms. These problems are the following: mutual exclusion, global snapshot recording, termination detection, deadlock detection, predicate detection, causal ordering, spanning tree construction, minimum spanning tree construction, all–all shortest paths computation, and maximal independent set computation. In a distributed algorithm, each process has access only to its local variables and incident edge parameters. We show the impossibility of solving these fundamental problems by proving that they require a solution to the causality determination problem which has been shown to be unsolvable in asynchronous message-passing distributed systems. Full article
(This article belongs to the Special Issue Graph Theory and Algorithmic Applications: Theoretical Developments)
17 pages, 345 KiB  
Article
Degree-Constrained Minimum Spanning Hierarchies in Graphs
by Miklos Molnar
Algorithms 2024, 17(10), 467; https://doi.org/10.3390/a17100467 - 21 Oct 2024
Cited by 1 | Viewed by 1239
Abstract
The minimum spanning tree problem in graphs under budget-type degree constraints (DCMST) is a well-known NP-hard problem. Spanning trees do not always exist, and the optimum can not be approximated within a constant factor. Recently, solutions have been proposed to solve degree-constrained spanning [...] Read more.
The minimum spanning tree problem in graphs under budget-type degree constraints (DCMST) is a well-known NP-hard problem. Spanning trees do not always exist, and the optimum can not be approximated within a constant factor. Recently, solutions have been proposed to solve degree-constrained spanning problems in the case of limited momentary capacities of the nodes. For a given node, the constraint represents a limited degree of the node for each visit. Finding the solution with minimum cost is NP-hard and the related algorithms are not trivial. This paper focuses on this new spanning problem with heterogeneous capacity-like degree bounds. The minimum cost solution corresponds to a graph-related structure, i.e., a hierarchy. We study the conditions of its existence, and we propose its exact computation, a heuristic algorithm, and its approximation. Full article
(This article belongs to the Special Issue Graph Theory and Algorithmic Applications: Theoretical Developments)
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