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Routing flow through a strongly connected graph

ALGORITHMICA 2002年第3期32卷 467-473页

作者： Erlebach, T Hagerup, T ETH Zurich Comp Engn & Networks Lab CH-8092 Zurich Switzerland Univ Frankfurt Inst Informat D-60054 Frankfurt Germany

It is shown that, for every strongly connected network in which every edge has capacity at least Delta, linear time suffices to send flow from source vertices, each with a given supply, to sink vertices, each with a given demand, provided that the total supply equals the total demand and is bounded by Delta. This problem arises in a maximum-flow algorithm of Goldberg and Rao, the binary blocking flow algorithm.

关键词： analysis of algorithms network flow maximum-flow problem feasible-flow problem strongly connected graph depth-first search

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Designing higher-dimensional digital chaotic systems via reverse derivation of iterative function from strongly connected graph and its application

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EXPERT SYSTEMS WITH APPLICATIONS 2024年 255卷

作者： Huang, Shufeng Wang, Qianxue Xiong, Xiaoming Cai, Shuting Guyeux, Christophe Guangdong Univ Technol Sch Integrated Circuits Guangzhou 510006 Peoples R China Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China Univ Bourgogne Franche Comte CNRS Femto ST Inst UMR 6174 F-25000 Besancon France

This paper describes a novel approach to designing higher-dimensional digital chaotic systems (HDDCSs). Using a strongly connected graph inverse approach, the resulting HDDCS is demonstrated to satisfy Devaney's definition of chaos. These HDDCSs are then efficiently implemented in digital circuits. Furthermore, we propose a novel method for generating measurement matrices using the designed HDDCS, which are utilized in compressive sensing-based image encryption techniques. Compared to traditional deterministic random matrices, the proposed HDDCS-based matrices offer significant improvements in terms of implementation efficiency, storage requirements, and robustness to noise. Experimental results show that our method achieves superior reconstruction outcomes and effectively obscures image correlations. This work not only contributes to the development of HDDCSs but also diversifies the methods for constructing measurement matrices in image encryption, providing a more secure and efficient alternative.

关键词： HDDCS strongly connected graph Circuit implementation Image encryption

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Constrained Cubic Grid Rigidity Decision with Directed graph and Applications

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2025年第2期205卷 1-23页

作者： Takacs, Anna Maria Katona, Janos Bajak, Szabolcs Kem, Gyula Nagy Budapest Business Univ Budapest Hungary Obuda Univ Budapest Hungary

We present a rigidity decision problem of constrained cubic grids in any given bracing pattern. The cubic grid bar and joint frameworks are not rigid. Additional constraints are required for rigidity. These constraints can be pinned down joints and additional bracing elements. Scaffoldings are not rigid cubic grid structures whose specific joints are pinned down. Inserting cable, strut, or rod bracing elements makes the framework rigid. Our model, which provides a linearly complex algorithm, has practical implications in testing the strong connectedness of a corresponding directed graph, contributing to the field of rigidity in structural engineering and motions of cable controlled pinned down cubic mechanisms.

关键词： Rigidity decision 3d grid Bar and joint structure Cable bracing strongly connected graph Tensegrities

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Globally Convergent Attitude Controlled Synchronization of Networked Spacecraft on strongly connected graphs

Globally Convergent Attitude Controlled Synchronization of N...

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31st Chinese Control Conference

作者： Wang, Hanlei Tan, Shuping Beijing Inst Control Engn Sci & Technol Space Intelligent Control Lab Beijing 100190 Peoples R China

ISBN: (纸本)9789881563811

In this paper, we address the attitude controlled synchronization problem for multiple networked spacecraft agents on strongly connected graphs. The nonlinear nature of the employed quaternion based attitude coupling distinguishes our result from most existing control schemes in the literature. We propose a new quaternion based inter-coupling control for networked spacecraft. Using this inter-coupling control, an cascaded adaptive control scheme is proposed. Using Lyapunov stability analysis, we show that the proposed adaptive controller is globally convergent and furthermore robust with respect to constant non-uniform time delays. Simulation results are presented to show the performance of the proposed control scheme.

关键词： Attitude synchronization strongly connected graph Time delay Euler parameter Adaptive control

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The Decomposition Problem for the Set of Paths in a Directed graph and Its Application

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AUTOMATION AND REMOTE CONTROL 2018年第12期79卷 2217-2236页

作者： Gainanov, D. N. Kibzun, A. I. Rasskazova, V. A. Natl State Univ Moscow Aviat Inst Moscow Russia

We consider the problem of decomposing the set of paths in a directed graph and its application to reducing the dimension of an applied problem on the assignment and transportation of locomotives. On a given set of paths and a set of strongly connected subgraphs, we define a special table. To solve the graph decomposition problem, we develop a heuristic algorithm based on the idea of quicksorting the constructed table. We estimate of the complexity of the resulting algorithm. The obtained results were used to reduce the dimension of the above-mentioned applied problem. We also show the results of computational experiments.

关键词： decomposition directed graph strongly connected graph algorithm locomotive assignment

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Efficiency of the principal eigenvector of some triple perturb e d consistent matrices

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第3期298卷 1007-1015页

作者： Fernandes, Rosario Furtado, Susana Univ Nova Lisboa Fac Ciencias & Tecnol CMA P-2829516 Caparica Portugal Univ Nova Lisboa Fac Ciencias & Tecnol Dept Matemat P-2829516 Caparica Portugal Univ Porto CEAFEL Rua Dr Roberto Frias P-4200464 Porto Portugal Univ Porto Fac Econ Rua Dr Roberto Frias P-4200464 Porto Portugal

In this paper we study the efficiency of the principal eigenvector of a pairwise comparison matrix ob-tained from a consistent one by perturbing three entries above the main diagonal, and the corresponding reciprocal entries, in a way that there is a submatrix of size 2 containing three of the perturbed entries and not containing a diagonal entry. Our approach uses the characterization of vector efficiency based on the strongly connection of a certain digraph associated with the matrix. By imposing some conditions on the magnitudes of the perturbations, we identify a class of matrices for which the principal eigenvector is efficient. This class is the union of two subclasses such that the digraph of all the matrices in the same subclass contains a common cycle with all vertices. The matrices we analyse include the simple perturbed consistent matrices, as well as a subfamily of the double perturbed consistent matrices, whose principal eigenvector efficiency has been studied in the literature. For completeness, we also include some exam-ples of triple perturbed matrices for which the principal eigenvector is not efficient. Explicit expressions for the characteristic polynomial and the principal eigenvector of the triple perturbed consistent matrices we consider are also given. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Decision processes Consistent matrix Pairwise comparison matrix Principal eigenvector efficiency strongly connected graph

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Convex polyhedral tilings hidden in crystals and quasicrystals

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REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS 2013年第1期107卷 123-143页

作者： Oda, Tadao Tohoku Univ Sendai Miyagi 980 Japan

Alattice in a Euclidean space gives rise to facet-to-facet and space-filling convex polyhedral tilings called the Voronoi tiling and its dual Delaunay tiling of the Euclidean space. Given a subspace of the Euclidean space, we develop a systematic way of constructing facet-to-facet and space-filling convex polyhedral tilings of the subspace called the Namikawa tilings, which are generalization of the Delaunay tiling. Our results here amplify the author's previous work with Seshadri that was obtained as a by-product of Geometric Invariant Theory in algebraic geometry. In the orthonormal setting where the lattice is spanned by an orthonormal basis of the ambient Euclidean space, the method of Namikawa tilings turns out to be the "cut and project" method relevant not only to periodic convex polyhedral tilings hidden in crystals but also to aperiodic convex polyhedral tilings hidden in quasicrystals. In another paper, the author showed that a Voronoi tiling is hidden in the "standard realization", in the sense of Kotani and Sunada, of crystals in the case of maximal abelian covering of finite graphs. In this connection, we give an affirmative answer to a question raised by Kotani to the effect that the crystal lies in the 1-skeleton of a nondegenerate convex polyhedral tiling that is a subdivision of the Voronoi tiling appearing in the other paper of the author.

关键词： Convex polyhedral tiling Cut and project method Crystal Quasicrystal strongly connected graph Geometric invariant theory

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Online Learning of Time-Varying Unbalanced Networks in Non-Convex Environments: A Multi-Armed Bandit Approach

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IEEE ACCESS 2023年 11卷 15567-15577页

作者： Odeyomi, Olusola T. North Carolina Agr & Tech State Univ Dept Comp Sci Greensboro NC 27411 USA

This study discusses how agents in a time-varying distributed network can converge to the global minimizer of a time-varying graph network. Each agent knows only the local loss of its observation and must cooperate constructively with other agents to find the global minimizer of the network. Unlike most existing works in the literature that consider a convex loss function, this study assumes a generalized local Lipschitz loss function for each agent, which can be convex or non-convex. We propose a multi-armed bandit algorithm CD EXP3 where each agent does not know its loss function but only observes its losses. Through simulations using two different time-varying graph topologies, we show that the algorithm helps all agents converge to the minimizer of the network. In addition, we discuss the effects of the two different topologies and various simulation parameters on convergence. We obtain an upper bound on the expected regret and compare it with the sublinearity of the regret bounds of well-known online distributed algorithms.

关键词： Online services Games Multi-armed bandit problem Probability distribution Noise measurement Network topology Knowledge engineering Online learning multi-armed bandit Lipschitz regret strongly connected graph

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CONSENSUS OF DISCRETE-TIME SECOND-ORDER MULTIAGENT SYSTEMS BASED ON INFINITE PRODUCTS OF GENERAL STOCHASTIC MATRICES

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2013年第4期51卷 3274-3301页

作者： Chen, Yao Lu, Jinhu Yu, Xinghuo Lin, Zongli Beijing Jiaotong Univ Sch Elect & Informat Engn Beijing 100044 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Inst Syst Sci Beijing 100190 Peoples R China RMIT Univ Sch Elect & Comp Engn Melbourne Vic 3001 Australia Univ Virginia Charles L Brown Dept Elect & Comp Engn Charlottesville VA 22904 USA

Traditionally, the consensus of a discrete-time multiagent system (MAS) with a switching topology is transformed into the convergence problem of the infinite products of stochastic matrices, which can be resolved by using the Wolfowitz theorem. However, such a transformation is very difficult or even impossible for certain MASs, such as discrete-time second-order MASs (DTSO MASs), whose consensus can only be transformed into the convergence problem of the infinite products of general stochastic matrices (IPGSM). These general stochastic matrices are matrices with row sum 1 but their elements are not necessarily nonnegative. Since there does not exist a general theory or an effective technique for dealing with the convergence of IPGSM, establishing the consensus criteria for a DTSO MAS with a switching topology is rather difficult. This paper concentrates on the consensus problem of a class of DTSO MASs and develops a method to cope with the corresponding IPGSM. Moreover, it is pointed out that the method for these DTSO MASs can also be easily extended to deal with a large class of discrete-time MASs, including high-order MASs with a switching topology and discrete-time MASs without velocity measurements.

关键词： second-order multiagent systems consensus strongly connected graph general stochastic matrix

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Globally Convergent Attitude Controlled Synchronization of Networked Spacecraft on strongly connected graphs

Globally Convergent Attitude Controlled Synchronization of N...

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第三十一届中国控制会议

作者： Hanlei Wang and Shuping Tan 1.Science and Technology on Space Intelligent Control Laboratory, Beijing Institute of Control Engineering,Beijing,100190,China.

In this paper,we address the attitude controlled synchronization problem for multiple networked spacecraft agents on strongly connected *** nonlinear nature of the employed quaternion based attitude coupling distinguishes our result from most existing control schemes in the *** propose a new quaternion based inter-coupling control for networked spacecraft. Using this inter-coupling control,an cascaded adaptive control scheme is *** Lyapunov stability analysis, we show that the proposed adaptive controller is globally convergent and furthermore robust with respect to constant non-uniform time *** results are presented to show the performance of the proposed control scheme.

关键词： Attitude synchronization strongly connected graph Time delay Euler parameter Adaptive control

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