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arXiv 2025年

作者： Alaoui, Ziad Ismaili Plump, Detlef University of Liverpool United Kingdom University of York United Kingdom

We report on a recent breakthrough in rule-based graph programming, which allows us to match the time complexity of some fundamental imperative graph algorithms. In general, achieving the complexity of graph algorithms in conventional languages using graph transformation rules is challenging due to the cost of graph matching. Previous work demonstrated that with rooted rules, certain algorithms can be implemented in the graph programming language GP 2 such that their runtime matches the time complexity of imperative implementations. However, this required input graphs to have a bounded node degree and (for some algorithms) to be connected. In this paper, we overcome these limitations by enhancing the graph data structure generated by the GP 2 compiler and exploiting the new structure in programs. We present three case studies: the first program checks whether input graphs are connected, the second program checks whether input graphs are acyclic, and the third program solves the single-source shortest-paths problem for graphs with integer edge-weights. The first two programs run in linear time on (possibly disconnected) input graphs with arbitrary node degrees. The third program runs in time O(mn) on arbitrary input graphs, matching the time complexity of imperative implementations of the Bellman-Ford algorithm. For each program, we formally prove its correctness and time complexity, and provide runtime experiments on various graph classes. © 2025, CC BY.

关键词： graph algorithms

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graph-Property Relationships for Complex Chiral Nanodendrimers

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ACS NANO 2025年第6期19卷 6095-6106页

作者： Kuznetsova, Vera Kadar, Alain Gaenko, Anita Er, Engin Ma, Tao Whisnant, Kody G. Ma, Jessica Ni, Bing Mehta, Natasha Kim, Ji-Young Gun'ko, Yurii K. Kotov, Nicholas A. Univ Michigan Dept Chem Engn Ann Arbor MI 48109 USA Univ Michigan Biointerfaces Inst Ann Arbor MI 48109 USA Univ Michigan Ctr Complex Particle Syst COMPASS Ann Arbor MI 48109 USA Rensselae Poly Tech Inst Chem & Biol Engn Troy NY 12180 USA Trinity Coll Dublin Sch Chem Dublin D02PN40 Ireland Univ Michigan Biotechnol Inst Ctr Complex Particle Syst COMPASS Michigan ND 48109 USA Univ Michigan Dept Mat Sci Ann Arbor MI 48109 USA

Organic, polymeric, and inorganic nanomaterials with radially diverging dendritic segments are known for their optical, physical, chemical, and biological properties inaccessible for traditional spheroidal particles. However, a methodology to quantitatively link their complex architecture to measurable properties is difficult due to the characteristically large degree of disorder, which is essential for observed property sets. Here, we address this conceptual problem using dendrimer-shaped gold particles with distinct stochastic branching and intense chiroptical activity using graph theory (GT). Unlike typical molecular or nanostructured dendrites, gold nanodendrimers are two-dimensional, with branches radially spreading within one plane. They are also chiral, with mirror asymmetry propagating through multiple scales. We demonstrate that their complex architecture is quantitatively described by image-informed GT models accounting for both regular and disordered structural components of the nanodendrimers. Furthermore, descriptors integrating topological and geometrical characteristics of particle graphs provide physics-based analytical relations to the nontrivial dependence of optical asymmetry g-factor on the particle structure. The simplicity of the GT models capable of capturing the complexity of the particle organization and related light-matter interactions enables the rapid design of scalable nanostructures with multiple functions.

关键词： chiral nanostructures fractals, complexity nonrandomness biomimetics self-assembly graph algorithms

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Two-Dimensional Balanced Partitioning and Efficient Caching for Distributed graph Analysis

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2025年第2期36卷 133-149页

作者： Lin, Shuai Wang, Rui Li, Yongkun Xu, Yinlong Lui, John C. S. Univ Sci & Technol China Hefei 230026 Peoples R China Zhejiang Univ Hangzhou 310027 Peoples R China Univ Sci & Technol China AnHui Prov Key Lab High Performance Comp Hefei 230026 Peoples R China Chinese Univ Hong Kong Hong Kong Peoples R China

Distributed graph analysis usually partitions a large graph into multiple small-sized subgraphs and distributes them into a cluster of machines for computing. Therefore, graph partitioning plays a crucial role in distributed graph analysis. However, the widely used existing graph partitioning schemes balance only in one dimension (number of edges or vertices) or incur a large number of edge cuts, so they degrade the performance of distributed graph analysis. In this article, we propose a novel graph partition scheme BPart and two enhanced algorithms BPart-C and BPart-S to achieve a balanced partition for both vertices and edges, and also reduce the number of edge cuts. Besides, we also propose a neighbor-aware caching scheme to further reduce the number of edge cuts so as to improve the efficiency of distributed graph analysis. Our experimental results show that BPart-C and BPart-S can achieve a better balance in both dimensions (the number of vertices and edges), and meanwhile reducing the number of edge cuts, compared to multiple existing graph partitioning algorithms, i.e., Chunk-V, Chunk-E, Fennel, and Hash. We also integrate these partitioning algorithms into two popular distributed graph systems, KnightKing and Gemini, to validate their impact on graph analysis efficiency. Results show that both BPart-C and BPart-S can significantly reduce the total running time of various graph applications by up to 60% and 70%, respectively. In addition, the neighbor-aware caching scheme can further improve the performance by up to 24%.

关键词： Partitioning algorithms Computational modeling Synchronization Costs Analytical models Social networking (online) Reviews Load modeling Clustering algorithms Blogs Distributed graph systems graph partition graph algorithms graph processing

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Research on Optimization Method of Landscape Architecture Planning and Design Based on Two-Dimensional Fractal graph Generation Algorithm

Informatica (Slovenia)

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Informatica (Slovenia) 2025年第16期49卷 53-66页

作者： Chen, Sheng Shanxi Vocational University of Engineering and Technology School of Architectural Design Department of Cultural Heritage Conservation Engineering China

The development of modern mathematical theory, especially two-dimensional fractal graph algorithm, provides a possibility for large-scale landscape data processing. Landscape digital identification technology is an innovative technology based on digital landscape technology and computer identification of experimental data. It is an important artificial intelligence technology, which includes three steps: landscape acquisition, landscape processing and landscape identification. The characteristics of the scene in the landscape picture can be collected by special instruments, such as cameras, etc., and then the collected data can be processed by two-dimensional fractal graph algorithm, and finally realice the automatic identification of the landscape. For images with significant boundary characteristics, we can extract the boundary of the región quickly and accurately, so as to realice the segmentation of the region. However, when the edge features of the image are not good enough, there is little color difference between the background and the region, or there is some interference, the result will be very bad. In this paper, based on the two-dimensional fractal graph generation algorithm, a series of optimization of landscape architecture planning and design. The accuracy of landscape prime number can reflect whether specific types of landscape pictures can be correctly identified and divided. 200 Pictures are divided into six categories, namely Water scene, landscape scene, living scene, sky scene, architecture and transportation then exact ratios of two-dimensional fractal graph network -8s, two-dimensional fractal graph network - 16s, two-dimensional fractal graph network -32s and two-dimensional fractal graph network -32s. It reached the best level in pixel accuracy, average accuracy, average IU, etc., and the pixel accuracy has reached as high as 100%, average accuracy has reached 100%, average accuracy has reached 100%. When compared to the recommended algorith

关键词： graph algorithms

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A Study of Intuitionistic Fuzzy graph Using Morphological Operators and Its Application

A Study of Intuitionistic Fuzzy Graph Using Morphological Op...

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International Conference on Mathematics of Intelligent Computing and Data Science, ICMICDS 2022

作者： Jacob, Abraham Ramkumar, P.B. Kerala Ernakulam India Department of Mathematics Rajagiri School of Engineering & Technology Kerala Ernakulam India

ISBN: (纸本)9789819615049

The study focuses on some properties of mathematical morphological operators on intuitionistic fuzzy graphs(IFG). Morphological operators like dilation and erosion and its composition are useful in the application of intuitionistic fuzzy graph. It is extended to study the topological properties using the topological data analysis(TDA) with the help of bar codes and betti numbers obtained by constructing minimal spanning trees(MST) which extracts topological properties of intuitionistic fuzzy graph. Finally, an algorithm for analyzing spread of disease is presented in this study. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： graph algorithms

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Protecting the Connectivity of a graph Under Non-Uniform Edge Failures 42

Protecting the Connectivity of a Graph Under Non-Uniform Edg...

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42nd International Symposium on Theoretical Aspects of Computer Science, STACS 2025

作者： Hommelsheim, Felix Liu, Zhenwei Megow, Nicole Zhang, Guochuan University of Bremen Germany Zhejiang University Hangzhou China

ISBN: (纸本)9783959773652

We study the problem of guaranteeing the connectivity of a given graph by protecting or strengthening edges. Herein, a protected edge is assumed to be robust and will not fail, which features a nonuniform failure model. We introduce the (p, q)-Steiner-Connectivity Preservation problem where we protect a minimum-cost set of edges such that the underlying graph maintains p-edge-connectivity between given terminal pairs against edge failures, assuming at most q unprotected edges can fail. We design polynomial-time exact algorithms for the cases where p and q are small and approximation algorithms for general values of p and q. Additionally, we show that when both p and q are part of the input, even deciding whether a given solution is feasible is NP-complete. This hardness also carries over to Flexible Network Design, a research direction that has gained significant attention. In particular, previous work focuses on problem settings where either p or q is constant, for which our new hardness result now provides justification. © Felix Hommelsheim, Zhenwei Liu, Nicole Megow, and Guochuan Zhang.

关键词： graph algorithms

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ReeSPOT: Reeb graph Models Semantic Patterns of Normalcy in Human Trajectories 27th

ReeSPOT: Reeb Graph Models Semantic Patterns of Normalcy in ...

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27th International Conference on Pattern Recognition, ICPR 2024

作者： Zhang, Bowen Shailja, S. Gudavalli, Chandrakanth Levenson, Connor Khan, Amil S. Manjunath, B. Electrical and Computer Engineering Department University of California Santa Barbara Santa Barbara United States

ISBN: (纸本)9783031781827

This paper introduces ReeSPOT, a novel Reeb graph-based method to model patterns of life in human trajectories (akin to a fingerprint). Human behavior typically follows a pattern of normalcy in day-to-day activities. This is marked by recurring activities within specific time periods. In this paper, we model this behavior using Reeb graphs where any deviation from usual day-to-day activities is encoded as nodes in the Reeb graph. The complexity of the proposed algorithm is linear with respect to the number of time points in a given trajectory. We demonstrate the usage of ReeSPOT and how it captures the critically significant spatial and temporal deviations using the nodes of the Reeb graph. Our case study presented in this paper includes realistic human movement scenarios: visiting uncommon locations, taking odd routes at infrequent times, uncommon time visits, and uncommon stay durations. We analyze the Reeb graph to interpret the topological structure of the GPS trajectories. Potential applications of ReeSPOT include urban planning, security surveillance, and behavioral research. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： graph algorithms

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Estimation of graph Features Based on Random Walks Using Neighbors’ Properties 25th

Estimation of Graph Features Based on Random Walks Using N...

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25th International Conference on Web Information Systems Engineering, WISE 2024

作者： Hasegawa, Tsuyoshi Hironaka, Shiori Shudo, Kazuyuki Kyoto University Yoshida-nihonmatsu-cho Kyoto Sakyo-ku606-8501 Japan

ISBN: (纸本)9789819605668

Using random walks for sampling has proven advantageous in assessing the characteristics of large and unknown social networks. Several algorithms based on random walks have been introduced in recent years. In the practical application of social network sampling, there is a recurrent reliance on an application programming interface (API) for obtaining adjacent nodes. However, owing to constraints related to query frequency and associated API expenses, it is preferable to minimize API calls during the feature estimation process. In this study, considering the acquisition of neighboring nodes as a cost factor, we introduce a feature estimation algorithm that outperforms existing algorithms in terms of accuracy. Through experiments that simulate sampling on known graphs, we demonstrate the superior accuracy of our proposed algorithm when compared to existing alternatives. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： graph algorithms

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The Par Clusterers Benchmark Suite (PCBS): A Fine-Grained Analysis of Scalable graph Clustering 51st

The Par Clusterers Benchmark Suite (PCBS): A Fine-Grained An...

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51st International Conference on Very Large Data Bases, VLDB 2025

作者： Yu, Shangdi Shi, Jessica Meindl, Jamison Eisenstat, David Ju, Xiaoen Tavakkol, Sasan Dhulipala, Laxman Lącki, Jakub Mirrokni, Vahab Shun, Julian MIT United States Google United States UMD United States

We introduce the Par Clusterers Benchmark Suite (PCBS)—a collection of highly scalable parallel graph clustering algorithms and benchmarking tools that streamline comparing different graph clustering algorithms and implementations. The benchmark includes clustering algorithms that target a wide range of modern clustering use cases, including community detection, classification, and dense sub graph mining. The benchmark toolkit makes it easy to run and evaluate multiple instances of different clustering algorithms with respect to both the running time and quality. We evaluate the PCBS algorithms empirically and find that they deliver both the state of the art quality and the running time. Interms of the running time, they are on average over 4x faster than the fastest library we compared to. In terms of quality, the correlation clustering algorithm [Shi et al., VLDB’21] optimizing for the Lambda CC objective, which does not have a direct counter part in other libraries, delivers the highest quality in the majority of datasets that we used. © 2025, VLDB Endowment, All rights reserved.

关键词： graph algorithms

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The Complexity of graph Exploration Games 50th

The Complexity of Graph Exploration Games

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50th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2025

作者： Fuchs, Janosch Grüne, Christoph Janßen, Tom Department of Computer Science RWTH Aachen University Aachen Germany

ISBN: (纸本)9783031826962

graph Exploration problems ask a searcher to explore an unknown environment. The environment is modeled as a graph, where the searcher needs to visit each vertex beginning at some vertex. Treasure Hunt problems are a variation of graph Exploration, in which the searcher needs to find a hidden treasure, which is located at a designated vertex. Usually these problems are modeled as online problems, and any online algorithm performs poorly because it has too little knowledge about the instance to react adequately to the requests of the adversary. Thus, the impact of a priori knowledge is of interest. One form of a priori knowledge is an unlabeled map, which is an isomorphic copy of the graph. We analyze graph Exploration and Treasure Hunt problems with an unlabeled map that is provided to the searcher. For this, we formulate decision variants of both problems by interpreting the online problems as a game between the online algorithm (the searcher) and the adversary. The map, however, is not controllable by the adversary. The question is whether the searcher is able to explore the graph completely or find the treasure for all possible decisions of the adversary. We analyze these games in multiple settings, with and without costs on the edges, on directed and undirected graphs and with different constraints (allowing multiple visits to vertices or edges) on the solution. We prove PSPACE-completeness for most of these games. Additionally, we analyze the complexity of related problems that have additional constraints on the solution. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： graph algorithms

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