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检索条件"主题词=Graph Algorithms"

共 2933 条记录，以下是201-210 订阅

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Spectra of Eccentricity Matrices of Product of graphs 11th

Spectra of Eccentricity Matrices of Product of Graphs

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11th International Conference on algorithms and Discrete Applied Mathematics, CALDAM 2025

作者： Balamoorthy, S. Kavaskar, T. Central University of Tamil Nadu Thiruvarur610 005 India

ISBN: (纸本)9783031834370

In this paper, we obtain the eccentricity spectrum and irreducibility of eccentricity matrix of the generalized friendship graph which is a generalization of the results in [12]. Also, we study the irreducibility of eccentricity matrix the H-join of graphs. As a consequence, we deduce a result in [12]. Further, we characterize graphs for which the eccentricity matrix of the generalized corona product of them is irreducible. As a result, we deduce a result in [11]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： graph algorithms

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Work Efficient Parallel algorithms for Large graph Exploration

Work Efficient Parallel Algorithms for Large Graph Explorati...

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20th International Conference on High Performance Computing (HiPC)

作者： Banerjee, Dip Sankar Sharma, Shashank Kothapalli, Kishore Int Inst Informat Technol Hyderabad 500032 Andhra Pradesh India

ISBN: (纸本)9781479907298

graph algorithms play a prominent role in several fields of sciences and engineering. Notable among them are graph traversal, finding the connected components of a graph, and computing shortest paths. There are several efficient implementations of the above problems on a variety of modern multiprocessor architectures. It can be noticed in recent times that the size of the graphs that correspond to real world data sets has been increasing. Parallelism offers only a limited succor to this situation as current parallel architectures have severe short-comings when deployed for most graph algorithms. At the same time, these graphs are also getting very sparse in nature. This calls for particular work efficient solutions aimed at processing large, sparse graphs on modern parallel architectures. In this paper, we introduce graph pruning as a technique that aims to reduce the size of the graph. Certain elements of the graph can be pruned depending on the nature of the computation. Once a solution is obtained for the pruned graph, the solution is extended to the entire graph. We apply the above technique on three fundamental graph algorithms: breadth first search (BFS), Connected Components (CC), and All Pairs Shortest Paths (APSP). To validate our technique, we implement our algorithms on a heterogeneous platform consisting of a multicore CPU and a GPU. On this platform, we achieve an average of 35% improvement compared to state-of-the-art solutions. Such an improvement has the potential to speed up other applications that rely on these algorithms.

关键词： MULTIPROCESSOR ARCHITECTURE Line graph EFFICIENT PARALLEL ALGORITHM Parallel algorithms graph algorithms Exploration connected component shortest path

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Optimizing Transitive Closure Computation for High Performance Computing and Security 33

Optimizing Transitive Closure Computation for High Performan...

引用

33rd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing, PDP 2025

作者： Masciari, Elio Napolitano, Enea Vincenzo DIETI University of Naples Federico II Naples Italy

ISBN: (纸本)9798331524937

Transitive closure computation is a fundamental operation in graph theory with applications in various domains. However, the increasing size and complexity of real-world graphs make traditional algorithms inefficient, especially when dealing with large datasets. This paper investigates the optimisation of transitive closure algorithms for high performance computing (HPC) applications. We implement and compare three different methods for computing the adjacency matrix of the transitive closure, based on three different Python libraries (NetworkX, PyTorch and NumPy). Our approach is benchmarked on seven real-world datasets of varying size and density to evaluate performance and scalability. The results show that NumPy achieves the best performance for large and dense graphs. The paper concludes with a discussion of the potential benefits of algorithmic optimization in HPC and security. © 2025 IEEE.

关键词： graph algorithms

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Lipschitz Continuous algorithms for graph Problems 64

Lipschitz Continuous Algorithms for Graph Problems

引用

64th Annual IEEE Symposium on the Foundations of Computer Science (FOCS)

作者： Kumabe, Soh Yoshida, Yuichi Univ Tokyo Grad Sch Informat Sci & Technol Tokyo Japan Natl Inst Informat Principles Informat Res Div Tokyo Japan

ISBN: (纸本)9798350318944

graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output changes can result in costly decisions, reduced user trust, potential security concerns, and lack of replicability. In this study, we consider the Lipschitz continuity of algorithms as a stability measure and initiate a systematic study of the Lipschitz continuity of algorithms for (weighted) graph problems. Depending on how we embed the output solution to a metric space, we can think of several Lipschitzness notions. We mainly consider the one that is invariant under scaling of weights, and we provide Lipschitz continuous algorithms and lower bounds for the minimum spanning tree problem, the shortest path problem, and the maximum weight matching problem. In particular, our shortest path algorithm is obtained by first designing an algorithm for unweighted graphs that are robust against edge contractions and then applying it to the unweighted graph constructed from the original weighted graph. Then, we consider another Lipschitzness notion induced by a natural mapping from the output solution to its characteristic vector. It turns out that no Lipschitz continuous algorithm exists for this Lipschitz notion, and we instead design algorithms with bounded pointwise Lipschitz constants for the minimum spanning tree problem and the maximum weight bipartite matching problem. Our algorithm for the latter problem is based on an LP relaxation with entropy regularization.

关键词： Approximation algorithms graph algorithms Lipschitz continuity Sensitivity

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Polylog-Competitive algorithms for Dynamic Balanced graph Partitioning for Ring Demands 23

Polylog-Competitive Algorithms for Dynamic Balanced Graph Pa...

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35th ACM Symposium on Parallelism in algorithms and Architectures (SPAA)

作者： Raecke, Harald Schmid, Stefan Zabrodin, Ruslan Tech Univ Munich Munich Germany Tech Univ Berlin Berlin Germany

ISBN: (纸本)9781450395458

The performance of many large-scale and data-intensive distributed systems critically depends on the capacity of the interconnecting network. This paper is motivated by the vision of self-adjusting infrastructures whose resources can be adjusted according to the workload they currently serve, in a demand-aware manner. Such dynamic adjustments can be exploited to improve network utilization and hence performance, by dynamically moving frequently interacting communication partners closer, e.g., collocating them in the same server or datacenter rack. In particular, we revisit the online balanced graph partitioning problem which captures the fundamental tradeoff between the benefits and costs of dynamically collocating communication partners. The demand is modelled as a sequence sigma(revealed in an online manner) of communication requests between.. processes, each of which is running on one of the l servers. Each server has capacity K = n/l, hence, the processes have to be scheduled in a balanced manner across the servers. A request incurs cost 1, if the requested processes are located on different servers, otherwise the cost is 0. A process can be migrated to a different server at cost 1. This paper presents the first online algorithm for online balanced graph partitioning achieving a polylogarithmic competitive ratio for the fundamental case of ring communication patterns. Specifically, our main contribution is a O( log(3)n)-competitive randomized online algorithm for this problem. We further present a randomized online algorithm which is O(log(2) n)-competitive when compared to a static optimal solution. Our two results rely on different algorithms and techniques and hence are of independent interest.

关键词： Online algorithms scheduling clustering graph partitioning graph algorithms

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A visual methodology to assess spatial graph vertex ordering algorithms 37

A visual methodology to assess spatial graph vertex ordering...

引用

37th SIBGRAPI Conference on graphics, Patterns and Images (SIBGRAPI)

作者： Salinas, Karelia Barella, Victor Vieira, Thales Nonato, Luis Gustavo Univ Sao Paulo ICMC USP Inst Math & Comp Sci Sao Carlos Brazil Fed Univ Alagoas UFAL Inst Comp Maceio Alagoas Brazil

ISBN: (纸本)9798350376043;9798350376036

graph vertex ordering is crucial for various graph-related applications, especially in spatial and urban data analysis where graphs represent real-world locations and their connections. The task is to arrange vertices along a single axis while preserving spatial relationships, but this often results in distortions due to the complexity of spatial data. Existing methods mostly assess ordering quality using a global metric, which may not capture specific use case needs or localized variations. This work proposes a new methodology to visually evaluate and compare vertex ordering techniques on spatial graphs. Two quantitative comparison mechanisms are proposed. Experiments on urban data from various cities demonstrate the methodology's effectiveness in tuning hyperparameters and comparing well-known vertex ordering techniques. The visual approach reveals nuanced spatial patterns that global metrics might miss, providing deeper insights into the behavior of different vertex ordering methods.

关键词： graph algorithms

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Approximation algorithms for graph Burning 1

引用

15th Annual Conference on Theory and Applications of Models of Computation (TAMC)

作者： Bonato, Anthony Kamali, Shahin Ryerson Univ Toronto ON Canada Univ Manitoba Winnipeg MB Canada

ISBN: (数字)9783030148126

ISBN: (纸本)9783030148119;9783030148126

Numerous approaches study the vulnerability of networks against social contagion. graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph. The burning process takes place in synchronous, discrete rounds. In each round, a fire breaks out at a vertex, and the fire spreads to all vertices that are adjacent to a burning vertex. The selection of vertices where fires start defines a schedule that indicates the number of rounds required to burn all vertices. Given a graph, the objective of an algorithm is to find a schedule that minimizes the number of rounds to burn graph. Finding the optimal schedule is known to be NP-hard, and the problem remains NP-hard when the graph is a tree or a set of disjoint paths. The only known algorithm is an approximation algorithm for disjoint paths, which has an approximation ratio of 1.5. We present approximation algorithms for graph burning. For general graphs, we introduce an algorithm with an approximation ratio of 3. When the graph is a tree, we present another algorithm with approximation ratio 2. Moreover, we consider a setting where the graph is a forest of disjoint paths. In this setting, when the number of paths is constant, we provide an optimal algorithm which runs in polynomial time. When the number of paths is more than a constant, we provide two approximation schemes: first, under a regularity condition where paths have asymptotically equal lengths, we show the problem admits an approximation scheme which is fully polynomial. Second, for a general setting where the regularity condition does not necessarily hold, we provide another approximation scheme which runs in time polynomial in the size of the graph.

关键词： Approximation algorithms graph algorithms graph burning problem Information dissemination Social contagion

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On hereditary graph classes defined by forbidding Truemper configurations: recognition and combinatorial optimization algorithms, and χ-boundedness results

On hereditary graph classes defined by forbidding Truemper c...

引用

作者： Boncompagni, Valerio The University of Leeds

学位级别：博士

Truemper configurations are four types of graphs that helped us understand the structure of several well-known hereditary graph classes. The most famous examples are perhaps the class of perfect graphs and the class of even-hole-free graphs: for both of them, some Truemper configurations are excluded (as induced subgraphs), and this fact appeared to be useful, and played some role in the proof of the known decomposition theorems for these classes. The main goal of this thesis is to contribute to the systematic exploration of hereditary graph classes defined by forbidding Truemper configurations. We study many of these classes, and we investigate their structure by applying the decomposition method. We then use our structural results to analyze the complexity of the maximum clique, maximum stable set and optimal coloring problems restricted to these classes. Finally, we provide polynomial-time recognition algorithms for all of these classes, and we obtain χ-boundedness results.

关键词： structural graph theory graph algorithms combinatorial optimization

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Evaluating the Influence of graph Characteristics on Parallel algorithms for Derived graph Structures 31

Evaluating the Influence of Graph Characteristics on Paralle...

引用

31st IEEE International Conference on High Performance Computing, Data, and Analytics Workshops, HiPCW 2024

作者： Pathak, Maulein Kapila, Samarth Sabharwal, Yogish Gupta, Neelima Dept of Computer Science University of Delhi India Keshav Mahavidyalaya University of Delhi India University Of British Columbia Vancouver Canada IBM Research India India Dept of Computer Science University of Delhi India

ISBN: (纸本)9798331509118

This work investigates how graph characteristics affect the quality of derived graphs, specifically focusing on graph spanners. graph spanners retain all vertices and a subset of edges while preserving shortest distances with an allowable stretch, making them essential for efficiently approximating graph structures. We emphasize recent advancements in parallel algorithms for constructing spanners in sparse graphs, building on the work of Miller et al. and Forster et al. By extracting key graph properties and employing data analysis techniques-such as correlation analysis, linear regression, and random forest regression-we examine the relationships between these characteristics and the size of the derived graphs, which is vital for optimizing spanner construction in real-world applications. © 2024 IEEE

关键词： graph algorithms

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Spherical graph Layout for Force-Directed algorithms 17

Spherical Graph Layout for Force-Directed Algorithms

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17th IEEE International Scientific Conference on Informatics, INFORMATICS 2024

作者： Mazuch, Martin Brezani, Alexander Kostolny, Jozef University of Žilina Faculty of Management Science and Informatics Žilina Slovakia

ISBN: (纸本)9798350387674

This article explores the difficulties and approaches related to arranging graphs in a spatial context, namely through the utilization of force-driven algorithms. These algorithms strive to decrease the overall energy of the system by strategically placing the vertices. An important difficulty arises when nodes are located outside the camera's field of view as a result of the application of different forces. One potential approach entails connecting a threads to each node, pulling it towards a central reference point to ensure that the complete network is visible inside the camera's field of view. The paper also underscores the intricacies of converting these algorithms from a two-dimensional to a three-dimensional context, underscoring the importance of preserving user comprehension while avoiding the concealment of information. The technique that is based on forces and connects the input graph with the physical system of forces is also referenced. © 2024 IEEE.

关键词： graph algorithms

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