Graph and Hypergraph Algorithms and 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: 31 October 2026 | Viewed by 2562

Special Issue Editor


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Guest Editor
Department of Education, Roma Tre University, 00185 Roma, Italy
Interests: graph and hypergraph algorithm; quantum computing; machine learning; computer vision

Special Issue Information

Dear Colleagues,

Graphs and hypergraphs are abstract structures able to capture a wide variety of real-world applications and can be used to solve problems arising from diverse fields ranging from artificial intelligence to network flows and from linear algebra to integer optimization problems, to cite only a few.

The aim of this Special Issue is to collect valuable, original and high quality papers on hypergraph and graph algorithms and applications.

Given the immense number of applications and the diverse fields in which graphs and hypergraphs are studied and applied, the scope of this Special Issue is very broad. It includes virtually any applicative field, apart from the traditional field of algorithms and data structure.

Topics of interest include but are not limited to the following, in which graphs or hypergraphs are the main tool for the problem or the application:

  • Optimization problems;
  • Quantum computing;
  • Computational complexity analysis;
  • Exact and approximation (hyper)graph algorithms;
  • Database systems;
  • Social Network Analysis;
  • Routing and shortest path;
  • Recommendation systems;
  • Graph neural networks.

Dr. Mauro Mezzini
Guest Editor

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Keywords

  • applications of hypergraphs and graphs
  • fast algorithms for special hypergraph and graph classes
  • design and analysis of hypergraph and graph algorithms
  • exact hypergraph and graph algorithms
  • approximation hypergraph and graph algorithms
  • computational complexity
  • fixed-parameter tractability
  • pattern matching in graphs
  • interconnection networks
  • social networks
  • telecommunication networks

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Published Papers (3 papers)

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Research

31 pages, 423 KiB  
Article
The Behavior of Tree-Width and Path-Width Under Graph Operations and Graph Transformations
by Frank Gurski and Robin Weishaupt
Algorithms 2025, 18(7), 386; https://doi.org/10.3390/a18070386 - 25 Jun 2025
Viewed by 124
Abstract
Tree-width and path-width are well-known graph parameters. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width and path-width under various unary and binary graph transformations. For [...] Read more.
Tree-width and path-width are well-known graph parameters. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width and path-width under various unary and binary graph transformations. For considered transformations, we provide upper and lower bounds for the tree-width and path-width of the resulting graph in terms of those of the initial graphs or argue why such bounds are impossible to specify. Among the studied unary transformations are vertex addition, vertex deletion, edge addition, edge deletion, subgraphs, vertex identification, edge contraction, edge subdivision, minors, powers of graphs, line graphs, edge complements, local complements, Seidel switching, and Seidel complementation. Among the studied binary transformations, we consider the disjoint union, join, union, substitution, graph product, 1-sum, and corona of two graphs. Full article
(This article belongs to the Special Issue Graph and Hypergraph Algorithms and Applications)
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11 pages, 537 KiB  
Article
The Clique-Width of Minimal Series-Parallel Digraphs
by Frank Gurski and Ruzayn Quaddoura
Algorithms 2025, 18(6), 323; https://doi.org/10.3390/a18060323 - 28 May 2025
Viewed by 211
Abstract
MSP DAGs (short for minimal series-parallel digraphs) can be defined from the single vertex graph by applying the parallel composition and series composition. We prove an upper bound of 6 for the directed clique-width of MSP DAGs and show how a directed clique-width [...] Read more.
MSP DAGs (short for minimal series-parallel digraphs) can be defined from the single vertex graph by applying the parallel composition and series composition. We prove an upper bound of 6 for the directed clique-width of MSP DAGs and show how a directed clique-width 6-expression can be found in linear time. Our 6-expression can be used to construct an MSP DAG G from its binary decomposition tree T(G) in linear time. We apply our bound on the directed clique-width to conclude a number of algorithmic consequences for MSP DAGs. Full article
(This article belongs to the Special Issue Graph and Hypergraph Algorithms and Applications)
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16 pages, 639 KiB  
Article
Geometric Methods and Computational Tools for Switching Structured Linear Systems
by Elena Zattoni, Anna Maria Perdon and Giuseppe Conte
Algorithms 2025, 18(4), 208; https://doi.org/10.3390/a18040208 - 8 Apr 2025
Viewed by 1598
Abstract
This work deals with switching structured linear systems, a class of structured linear systems whose existing links between the state, input, and output variables have unknown numerical values and, in addition, are subject to change according to an exogenous, time-dependent signal. Geometric methods [...] Read more.
This work deals with switching structured linear systems, a class of structured linear systems whose existing links between the state, input, and output variables have unknown numerical values and, in addition, are subject to change according to an exogenous, time-dependent signal. Geometric methods and computational tools developed to solve control and observation problems stated for this class of structured linear systems are presented. In particular, this work delves into the notions of invariance, controlled invariance, and conditioned invariance and focuses on their use in the statement and proof of conditions for the solvability of the disturbance decoupling problem, both by state feedback and by output feedback, and of the unknown-input state observation problem. The fundamental concepts and the main results are explained using handy examples, with visual aid provided by directed graphs. Full article
(This article belongs to the Special Issue Graph and Hypergraph Algorithms and Applications)
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