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Finite-Time distributed algorithms for Verifying and Ensuring Strong Connectivity of Directed Networks

IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2022年第6期9卷 4379-4392页

作者： Atman, Made Widhi Surya Gusrialdi, Azwirman Tampere Univ Fac Engn & Nat Sci Tampere 33014 Finland

The strong connectivity of a directed graph associated with the communication network topology is crucial in ensuring the convergence of many distributed estimation/control/optimization algorithms. However, the assumption on the network's strong connectivity may not always be satisfied in practice. In addition, information on the overall network topology is often not available, e.g., due to privacy concerns or geographical constraints which calls for a distributed algorithm. This paper aims to fill a crucial gap in the literature due to the absence of a fully distributed algorithm to verify and ensure in finite-time the strong connectivity of a directed network. Specifically, inspired by the maximum consensus algorithm we propose distributed algorithms that enable individual node in a networked system to verify the strong connectivity of a directed graph and further, if necessary, augment a minimum number of new links to ensure the directed graph's strong connectivity. The proposed distributed algorithms are implemented without requiring information of the overall network topology and are scalable as they only require finite storage and converge in finite number of steps. Furthermore, the algorithms also preserve the privacy in terms of the overall network's topology. Finally, the proposed distributed algorithms are demonstrated and evaluated via numerical results.

关键词： Network topology distributed algorithms Directed graphs Topology Communication networks Privacy Optimization distributed algorithms finite-time link addition max-consensus strongly connected digraph weakly connected digraph

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Designing distributed algorithms for mobile computing networks

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COMPUTER COMMUNICATIONS 1996年第4期19卷 309-320页

作者： Badrinath, BR Acharya, A Imielinski, T Department of Computer Science Rutgers University New Brunswick NJ 08903 USA

Mobile computing represents a new paradigm that aims to provide continuous network connectivity to users regardless of their location. To realize this aim, it is necessary to design distributed algorithms that explicitly account for host mobility and the physical constraints associated with such networks. This paper presents an operational system model for explicitly incorporating the effects of host mobility with appropriate cost measures. It points out the drawbacks of executing distributed algorithms in this model that are not explicitly designed for mobile hosts. To overcome the resource constraints of mobile hosts, we propose a two tier principle for structuring distributed algorithms for mobile hosts so that the computation and communication requirements of an algorithm are borne by the static hosts to the extent possible. In addition, since location of a mobile host could change after initiating a distributed computation and before receiving the result, location management of mobile participants needs to be explicitly integrated with algorithm design.

关键词： mobile computing distributed algorithms two tier principle

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Continuous distributed algorithms for solving linear equations in finite time

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AUTOMATICA 2020年第0期113卷 108755-000页

作者： Shi, Xinli Yu, Xinghuo Cao, Jinde Wen, Guanghui Southeast Univ Sch Cyber Sci & Engn Nanjing 210096 Peoples R China RMIT Univ Sch Engn Melbourne Vic 3001 Australia Southeast Univ Sch Math Nanjing 210096 Peoples R China

This paper studies the distributed algorithms to obtain a solution of the linear equation Ax = b in finite time (FT) over a multi-agent network. In order to guarantee the settling time without depending on the initial states, the fixed-time (FxT) distributed algorithms are also provided to obtain a solution within a globally bounded time. Specifically, three distributed nonlinear algorithms are developed. The first one is designed to achieve FT/FxT consensus on a solution with special initialization. The second is to obtain the solution in FT/FxT with free initialization by first driving the local states to satisfy the special initialization in FT/FxT time. The last one is to guarantee the FT/FxT convergence to a solution closest to specific points when multiple solutions exist. Finally, three case studies are performed to show the effectiveness of the proposed algorithms. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： distributed algorithms Finite/fixed-time consensus Multi-agent networks Linear equations

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Fast distributed algorithms for computing separable functions

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IEEE TRANSACTIONS ON INFORMATION THEORY 2008年第7期54卷 2997-3007页

作者： Mosk-Aoyama, Damon Shah, Devavrat Stanford Univ Dept Elect Engn & Comp Sci Stanford CA 94305 USA MIT Dept Elect Engn & Comp Sci Cambridge MA 02139 USA

The problem of computing functions of values at the nodes in a network in a fully distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer, and ad hoc networks. The task of computing separable functions, which can be written as linear combinations of functions of individual variables, is studied in this context. Known iterative algorithms for averaging can be used to compute the normalized values of such functions, but these algorithms do not extend, in general, to the computation of the actual values of separable functions. The main contribution of this paper is the design of a distributed randomized algorithm for computing separable functions. The running time of the algorithm is shown to depend on the running time of a minimum computation algorithm used as a subroutine. Using a randomized gossip mechanism for minimum computation as the subroutine yields a complete fully distributed algorithm for computing separable functions. For a class of graphs with small spectral gap, such as grid graphs, the time used by the algorithm to compute averages is of a smaller order than the time required by a known iterative averaging scheme.

关键词： data aggregation distributed algorithms gossip algorithms randomized algorithms

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IMPROVING THE TIME-COMPLEXITY OF MESSAGE-OPTIMAL distributed algorithms FOR MINIMUM-WEIGHT SPANNING-TREES: 收藏
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引用; SIAM JOURNAL ON COMPUTING 1990年第4期19卷 612-626页; 作者： CHIN, F TING, HF PRINCETON UNIV DEPT COMP SCIPRINCETONNJ 08544; A distributed algorithm is presented that constructs the minimum-weight spanning tree of an undirected connected graph with distinct node identities. Initially, each node knows only the weight of each of its adjacent ... 详细信息; A distributed algorithm is presented that constructs the minimum-weight spanning tree of an undirected connected graph with distinct node identities. Initially, each node knows only the weight of each of its adjacent edges. When the algorithm terminates, each node knows which of its adjacent edges are edges of the tree. For a graph with n nodes and e edges, the total number of messages required by this algorithm is at most $5 n \log n + 2 e$; 来源：评论; 学校读者我要写书评

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Optimal distributed algorithms in unlabeled tori and chordal rings

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JOURNAL OF PARALLEL AND distributed COMPUTING 1997年第1期46卷 80-90页

作者： Mans, B Macquarie Univ Sch Math Phys Comp & Elect Dept Comp Sydney NSW 2109 Australia

We study the message complexity of distributed algorithms in tori and chordal Rings when the communication links are unlabeled, which implies that the processors do not have "sense of direction." We introduce the paradigm of handrail which allows messages to travel with a consistent direction. We give a distributed algorithm which confirms the conjecture that the leader election problem for unlabeled tori of N processors can be solved using Theta(N) messages instead of O(N log N), Using the same handrail paradigm, we solve the election problem using Theta(N) messages in unlabeled chordal rings with one chord (of length approximately root N). This solves the long-standing open problem of the minimal number of unlabeled chords required to decrease the O(N log N). message complexity, For each topology, we give an algorithm to compute the sense of direction in Theta(N) messages (improving the O(N log N) previous results), This proves the more fundamental result that any global distributed algorithm for these labeled topologies can be used with a similar asymptotic complexity in the respective unlabeled class. (C) 1997 Academic Press.

关键词： Complete network Hypercubes Elections Direction Sense PROCESSOR Tori sense of direction Messages communication complexity RAILINGS Telecommunication links Hypercube Chord distributed algorithms

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Column Partition Based distributed algorithms for Coupled Convex Sparse Optimization: Dual and Exact Regularization Approaches

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IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS 2021年 7卷 375-391页

作者： Shen, Jinglai Hu, Jianghai Kammara, Eswar Kumar Hathibelagal Univ Maryland Baltimore Cty Dept Math & Stat Baltimore MD 21250 USA Purdue Univ Sch Elect & Comp Engn W Lafayette IN 47907 USA

This paper develops column partition based distributed schemes for a class of convex sparse optimization problems, e.g., basis pursuit (BP), LASSO, basis pursuit denosing (BPDN), and their extensions, e.g., fused LASSO. We are particularly interested in the cases where the number of (scalar) decision variables is much larger than the number of (scalar) measurements, and each agent has limited memory or computing capacity such that it only knows a small number of columns of a measurement matrix. The problems in consideration are densely coupled and cannot be formulated as separable convex programs. To overcome this difficulty, we consider their dual problems which are separable or locally coupled. Once a dual solution is attained, it is shown that a primal solution can be found from the dual of corresponding regularized BP-like problems under suitable exact regularization conditions. A wide range of existing distributed schemes can be exploited to solve the obtained dual problems. This yields two-stage column partition based distributed schemes for LASSO-like and BPDN-like problems;the overall convergence of these schemes is established. Numerical results illustrate the performance of the proposed two-stage distributed schemes.

关键词： Information processing Optimization Indexes distributed algorithms Convergence Standards Noise reduction Sparse optimization distributed computation duality theory exact regularization sensitivity analysis

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Asynchronous distributed algorithms for Seeking Generalized Nash Equilibria Under Full and Partial-Decision Information

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IEEE TRANSACTIONS ON CYBERNETICS 2020年第6期50卷 2514-2526页

作者： Yi, Peng Pavel, Lacra Washington Univ Dept Elect & Syst Engn St Louis MO 63130 USA Univ Toronto Dept Elect & Comp Engn Toronto ON M5S 3G9 Canada

This paper investigates asynchronous algorithms for distributedly seeking generalized Nash equilibria with delayed information in multiagent networks. In the game model, a shared affine constraint couples all players' local decisions. Each player is assumed to only access its private objective function, private feasible set, and a local block matrix of the affine constraint. We first give an algorithm for the case when each agent is able to fully access all other players' decisions. By using auxiliary variables related to communication links and the edge Laplacian matrix, each player can carry on its iteration asynchronously with only private data and possibly delayed information from its neighbors. Then, we consider the case when agents cannot know all other players' decisions, called a partial-decision information case. We introduce a local estimation of the overall agents' decisions and incorporate consensus dynamics on these local estimations. The two algorithms do not need any centralized clock coordination, fully exploit the local computation resource, and remove the idle time due to waiting for the "slowest" agent. Both algorithms are developed by preconditioned forward-backward operator splitting, and their convergence is shown by relating them to asynchronous fixed-point iterations, under proper assumptions and fixed and nondiminishing step-size choices. Numerical studies verify the algorithms' convergence and efficiency.

关键词： Games Convergence Heuristic algorithms distributed algorithms Linear programming Estimation Couplings Asynchronous computation distributed algorithm generalized Nash equilibrium (GNE) monotone game multiagent systems operator splitting methods

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Compositional competitiveness for distributed algorithms

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JOURNAL OF algorithms-COGNITION INFORMATICS AND LOGIC 2005年第2期54卷 127-151页

作者： Aspnes, J Waarts, O Yale Univ Dept Comp Sci New Haven CT 06520 USA Univ Calif Berkeley Div Comp Sci Berkeley CA USA

We define a measure of competitive performance for distributed algorithms based on throughput, the number of tasks that an algorithm can carry out in a fixed amount of work. This new measure complements the latency measure of Ajtai et al. [A theory of competitive analysis for distributed algorithms, in: 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, IEEE, 1994, pp. 401-411]. which measures how quickly an algorithm can finish tasks that start at specified times. The novel feature of the throughput measure, which distinguishes it from the latency measure, is that it is compositional: it supports a notion of algorithms that are competitive relative to a class of subroutines, with the property that an algorithm that is k-competitive relative to a class of subroutines, combined with an l-competitive member of that class, gives a combined algorithm that is kl-competitive. In particular, we prove the throughput-competitiveness of a class of algorithms for collect operations, in which each of a group of n processes obtains all values stored in an array of n registers.

关键词： distributed algorithms shared memory competitive analysis

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Fast distributed algorithms for Brooks-Vizing colorings

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JOURNAL OF algorithms 2000年第1期37卷 85-120页

作者： Grable, DA Panconesi, A Humboldt Univ Inst Informat D-10099 Berlin Germany Univ Bologna I-40127 Bologna Italy

Let G be a Delta-regular graph with n vertices and girth at least 4 such that Delta much greater than log n. We give very simple, randomized, distributed algorithms for vertex coloring G with Delta/k colors in O(k + log n) communication rounds, where k = O(log Delta). The algorithm may fail or exceed the above running time, but the probability that this happens is o(1), a quantity that goes to zero as n grows. The probabilistic analysis relies on a powerful generalization of Azuma's martingale inequality that we dub the Method of Bounded Variances. (C) 2000 Academic Press.

关键词： Parallel Probabilistic analysis Color logarithm (log) vertex head delta Parallel Lines GIRTH Delta distributed algorithms Runtime

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