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15 pages, 444 KB

Open AccessArticle

Steiner Tree Approximations in Graphs and Hypergraphs

by Miklós Molnár and Basma Mostafa Hassan

Algorithms 2026, 19(3), 232; https://doi.org/10.3390/a19030232 - 19 Mar 2026

Viewed by 385

Abstract

The construction of partial minimum spanning trees is an NP-hard problem, leading to the development of various heuristic algorithms. Existing heuristics, including Kruskal’s algorithm, frequently employ shortest paths to connect tree components. This study introduces an approximate algorithm for constructing the minimum Steiner [...] Read more.

The construction of partial minimum spanning trees is an NP-hard problem, leading to the development of various heuristic algorithms. Existing heuristics, including Kruskal’s algorithm, frequently employ shortest paths to connect tree components. This study introduces an approximate algorithm for constructing the minimum Steiner tree, which serves as the optimal structure for diffusion multicast. The proposed approach utilizes graph-based structures that provide advantages over conventional shortest-path methods. The algorithm incorporates connections analogous to those in simple Steiner trees when required. These simple trees are represented by hyperedges, and a Hyper Metric Closure can also be applied. Experimental results indicate that this hypergraph-based method enables constructions that more closely approximate the optimal Steiner tree cost compared to traditional pairwise techniques, offering a scalable balance between computational complexity and routing efficiency. Full article

(This article belongs to the Special Issue Graph and Hypergraph Algorithms and Applications)

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16 pages, 401 KB

Open AccessArticle

Heuristic Conductance-Aware Local Clustering for Heterogeneous Hypergraphs

by Jingtian Wei, Xuan Li and Hongen Lu

Algorithms 2026, 19(1), 79; https://doi.org/10.3390/a19010079 - 16 Jan 2026

Viewed by 363

Abstract

Graphs are widely used to model complex interactions among entities, yet they struggle to capture higher-order and multi-typed relationships. Hypergraphs overcome this limitation by allowing for edges to connect arbitrary sets of nodes, enabling richer modelling of higher-order semantics. Real-world systems, however, often [...] Read more.

Graphs are widely used to model complex interactions among entities, yet they struggle to capture higher-order and multi-typed relationships. Hypergraphs overcome this limitation by allowing for edges to connect arbitrary sets of nodes, enabling richer modelling of higher-order semantics. Real-world systems, however, often exhibit heterogeneity in both entities and relations, motivating the need for heterogeneous hypergraphs as a more expressive structure. In this study, we address the problem of local clustering on heterogeneous hypergraphs, where the goal is to identify a semantically meaningful cluster around a given seed node while accounting for type diversity. Existing methods typically ignore node-type information, resulting in clusters with poor semantic coherence. To overcome this, we propose HHLC, a heuristic heterogeneous hyperedge-based local clustering algorithm, guided by a heterogeneity-aware conductance measure that integrates structural connectivity and node-type consistency. HHLC employs type-filtered expansion, cross-type penalties, and low-quality hyperedge pruning to produce interpretable and compact clusters. Comprehensive experiments on synthetic and real-world heterogeneous datasets demonstrate that HHLC consistently outperforms strong baselines across metrics such as conductance, semantic purity, and type diversity. These results highlight the importance of incorporating heterogeneity into hypergraph algorithms and position HHLC as a robust framework for semantically grounded local analysis in complex multi-relational networks. Full article

(This article belongs to the Special Issue Graph and Hypergraph Algorithms and Applications)

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27 pages, 6190 KB

Open AccessArticle

Multimodal Temporal Fusion for Next POI Recommendation

by Fang Liu, Jiangtao Li and Tianrui Li

Algorithms 2026, 19(1), 3; https://doi.org/10.3390/a19010003 - 20 Dec 2025

Viewed by 670

Abstract

The objective of the next POI recommendation is using the historical check-in sequences of users to learn the preferences and habits of users, providing a list of POIs that users will be inclined to visit next. Then, there are some limitations in existing [...] Read more.

The objective of the next POI recommendation is using the historical check-in sequences of users to learn the preferences and habits of users, providing a list of POIs that users will be inclined to visit next. Then, there are some limitations in existing POI recommendation algorithms. On the one hand, after obtaining the user’s preferences for the current period, if we consider the entire historical check-in sequence, including future check-in information, it is susceptible to the influence of noisy data, thereby reducing the accuracy of recommendations. On the other hand, the current methods generally rely on modeling long- and short-term preferences within a fixed time window, which possibly leads to an inability to capture users’ behavior characteristics at different time scales. As a result, we proposed a Multimodal Temporal Fusion for Next POI Recommendation(MTFNR). Firstly, to understand users’ preferences and habits at different periods, multiple hypergraph neural networks are constructed to analyze user behavior patterns at different stages, and in order to avoid introducing interference factors, only the check-in sequences visited in the current period are considered to reduce the impact of noise on the model’s recommendation performance. Secondly, modeling the next POI recommendation task through the fusion of time information and long- and short-term preferences in order to gain a more comprehensive understanding of users’ preferences and habits, enhance the timeliness of recommendations, and improve the accuracy of recommendations. Lastly, introducing spatio-temporal interval information into the GRU model, capturing dependencies in sequences to improve the overall performance of the model. Extensive experiments on the real LBSN datasets demonstrated the superior performance of the MTFNR model. The experimental results indicate that Top-10 recall improved 2.81% to 15.97% compared to current methods. Full article

(This article belongs to the Special Issue Graph and Hypergraph Algorithms and Applications)

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22 pages, 1524 KB

Open AccessArticle

Hypergraph Neural Networks for Coalition Formation Under Uncertainty

by Gerasimos Koresis, Charilaos Akasiadis and Georgios Chalkiadakis

Algorithms 2025, 18(11), 724; https://doi.org/10.3390/a18110724 - 17 Nov 2025

Viewed by 940

Abstract

Identifying effective coalitions of agents for task execution within large multiagent settings is a challenging endeavor. The problem is exacerbated by the presence of coalitional value uncertainty, which is due to uncertainty regarding the values of synergies among the different collaborating agent types. [...] Read more.

Identifying effective coalitions of agents for task execution within large multiagent settings is a challenging endeavor. The problem is exacerbated by the presence of coalitional value uncertainty, which is due to uncertainty regarding the values of synergies among the different collaborating agent types. Intuitively, in such environments, a hypergraph can be used to concisely represent coalition–task pairs in the form of hyperedges, along with their associated rewards. Therefore, this paper proposes harnessing the power of Hypergraph Neural Networks (HGNNs) that fit generic hypergraph-structured historical representations of coalitional task executions to learn the unknown values of coalitional configurations undertaking the tasks. However, the fitted model by itself cannot be used to provide suggestions on which coalitions to form; it can only be queried for the values of given coalition–task configurations. To actually provide coalitional suggestions, this work relies on informed search approaches that incorporate the output of the HGNN as an indicator of the quality of the proposed coalition configurations. The resulting approach is illustrated, via simulation results, to be able to effectively capture the uncertain values of multiagent synergies and thus suggest highly rewarding coalitional configurations. Specifically, the proposed novel hybrid approach can outperform competing baseline approaches and achieve close to 80% performance of the theoretical maximum in this setting. Full article

(This article belongs to the Special Issue Graph and Hypergraph Algorithms and Applications)

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19 pages, 439 KB

Open AccessEditor’s ChoiceArticle

Speeding Up Floyd–Warshall’s Algorithm to Compute All-Pairs Shortest Paths and the Transitive Closure of a Graph

by Giuseppe Lancia and Marcello Dalpasso

Algorithms 2025, 18(9), 560; https://doi.org/10.3390/a18090560 - 4 Sep 2025

Cited by 3 | Viewed by 3013

Abstract

Floyd–Warshall’s algorithm is a widely-known procedure for computing all-pairs shortest paths in a graph of n vertices in

Θ (n^{3})

time complexity. A simplified version of the same algorithm computes the transitive closure of the graph with the same time [...] Read more.

Floyd–Warshall’s algorithm is a widely-known procedure for computing all-pairs shortest paths in a graph of n vertices in

Θ (n^{3})

time complexity. A simplified version of the same algorithm computes the transitive closure of the graph with the same time complexity. The algorithm operates on an

n \times n

matrix, performing n inspections and no more than n updates of each matrix cell, until the final matrix is computed. In this paper, we apply a technique called SmartForce, originally devised as a performance enhancement for solving the traveling salesman problem, to avoid the inspection and checking of cells that do not need to be updated, thus reducing the overall computation time when the number, u, of cell updates is substantially smaller than

n^{3}

. When the ratio

u / n^{3}

is not small enough, the performance of the proposed procedure might be worse than that of the Floyd–Warshall algorithm. To speed up the algorithm independently of the input instance type, we introduce an effective hybrid approach. Finally, a similar procedure, which exploits suitable fast data structures, can be used to achieve a speedup over the Floyd–Warshall simplified algorithm that computes the transitive closure of a graph. Full article

(This article belongs to the Special Issue Graph and Hypergraph Algorithms and Applications)

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31 pages, 423 KB

Open AccessArticle

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 3685

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 KB

Open AccessArticle

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 1057

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 KB

Open AccessArticle

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 2230

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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20 pages, 817 KB

Open AccessEditor’s ChoiceSystematic Review

Domain-Specific Languages for Algorithmic Graph Processing: A Systematic Literature Review

by Houda Boukham, Kawtar Younsi Dahbi and Dalila Chiadmi

Algorithms 2025, 18(7), 445; https://doi.org/10.3390/a18070445 - 19 Jul 2025

Viewed by 2099

Abstract

Graph analytics has grown increasingly popular as a model for data analytics across a variety of domains. This has prompted an emergence of solutions for large-scale graph analytics, many of which integrate user-facing domain-specific languages (DSLs) to support graph processing operations. These DSLs [...] Read more.

Graph analytics has grown increasingly popular as a model for data analytics across a variety of domains. This has prompted an emergence of solutions for large-scale graph analytics, many of which integrate user-facing domain-specific languages (DSLs) to support graph processing operations. These DSLs fall into two categories: query-based DSLs for graph-pattern matching and graph algorithm DSLs. While graph query DSLs are now standardized, research on DSLs for algorithmic graph processing remains fragmented and lacks a cohesive framework. To address this gap, we conduct a systematic literature review of algorithmic graph processing DSLs aimed at large-scale graph analytics. Our findings reveal the prevalence of property graphs (with 60% of surveyed DSLs explicitly adopting this model), as well as notable similarities in syntax and features. This allows us to identify a common template that can serve as the foundation for a standardized graph algorithm model, improving portability and unifying design between different DSLs and graph analytics toolkits. We additionally find that, despite achieving remarkable performance and scalability, only 20% of surveyed DSLs see real-life adoption. Incidentally, all DSLs for which user documentation is available are developed as part of academia–industry collaborations or in fully industrial contexts. Based on these results, we provide a comprehensive overview of the current research landscape, along with a roadmap of recommendations and future directions to enhance reusability and interoperability in large-scale graph analytics across industry and academia. Full article

(This article belongs to the Special Issue Graph and Hypergraph Algorithms and Applications)

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