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 ...
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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 5nlogn+2
68M10
68Q25
distributed algorithms
synchronous and asynchronous networks
minimum spanning trees
communication complexity
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 s...
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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.
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...
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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.
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 LASS...
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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.
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 me...
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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.
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&...
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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.
This paper introduces distributed algorithms that share the power generation task in an optimized fashion among the several distributed Energy Resources (DERs) within a microgrid. We borrow certain concepts from commu...
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This paper introduces distributed algorithms that share the power generation task in an optimized fashion among the several distributed Energy Resources (DERs) within a microgrid. We borrow certain concepts from communication network theory, namely Additive-Increase-Multiplicative-Decrease (AIMD) algorithms, which are known to be convenient in terms of communication requirements and network efficiency. We adapt the synchronized version of AIMD to minimize a cost utility function of interest in the framework of smart grids. We then implement the AIMD utility optimisation strategies in a realistic power network simulation in Matlab-OpenDSS environment, and we show that the performance is very close to the full-communication centralized case.
The issue of correctness of complex asynchronous distributed algorithms implemented on loosely coupled parallel processor systemsis difficult to address given the lack of effective debugging tools. In such systems, me...
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The issue of correctness of complex asynchronous distributed algorithms implemented on loosely coupled parallel processor systemsis difficult to address given the lack of effective debugging tools. In such systems, messages propagate asynchronously over physical connections and precise knowledge of the state of every message in the system at any instant of time is difficult to obtain. For a particular class of asynchronous distributed algorithms [1,2,5] that may be characterized by independent models that execute asynchronously on the processors and interact with one another only through explicit messages, the following reasoning applies. Information on the flow and content of messages and the activity of the processors is significant towards understanding the functional correctness of the implementation. This paper proposes a new approach, MADCAPP, to measure and analyze high-level message communication and the activity level of the processors.
For a given graph G over n vertices, let OPTG denote the size of an optimal solution in G of a particular minimization problem (e.g., the size of a minimum vertex cover). A randomized algorithm will be called an alpha...
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For a given graph G over n vertices, let OPTG denote the size of an optimal solution in G of a particular minimization problem (e.g., the size of a minimum vertex cover). A randomized algorithm will be called an alpha-approximation algorithm with an additive error for this minimization problem if for any given additive error parameter epsilon > 0 it computes a value (OPT) over tilde such that, with probability at least 2/3, it holds that OPTG <= (OPT) over tilde <= alpha .OPTG + epsilon n. Assume that the maximum degree or average degree of G is bounded. In this case, we show a reduction from local distributed approximation algorithms for the vertex cover problem to sublinear approximation algorithms for this problem. This reduction can be modified easily and applied to other optimization problems that have local distributed approximation algorithms, such as the dominating set problem. We also show that for the minimum vertex cover problem, the query complexity of such approximation algorithms must grow at least linearly with the average degree (d) over bar of the graph. This lower bound holds for every multiplicative factor alpha and small constant epsilon as long as (d) over bar = O(n/alpha). In particular this means that for dense graphs it is not possible to design an algorithm whose complexity is o(n). (c) 2007 Elsevier B.V. All rights reserved.
Two asynchronous distributed algorithms are presented for solving a linear equation of the form Ax = b with at least one solution. The equation is simultaneously and asynchronously solved by m agents assuming that eac...
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Two asynchronous distributed algorithms are presented for solving a linear equation of the form Ax = b with at least one solution. The equation is simultaneously and asynchronously solved by m agents assuming that each agent knows only a subset of the rows of the partitioned matrix [A b], the estimates of the equation's solution generated by its neighbors, and nothing more. Neighbor relationships are characterized by a time-dependent directed graph whose vertices correspond to agents and whose arcs depict neighbor relationships. Each agent recursively updates its estimate of a solution at its own event times by utilizing estimates generated by its neighbors which are transmitted with delays. The event time sequences of different agents are not assumed to be synchronized. It is shown that for any matrix-vector pair (A, b) for which the equation has a solution and any repeatedly jointly strongly connected sequence of neighbor graphs defined on the merged sequence of all agents' event times, the algorithms cause all agents' estimates to converge exponentially fast to the same solution to Ax = b. The first algorithm requires a specific initialization step at each agent, and the second algorithm works for arbitrary initializations. Explicit expressions for convergence rates are provided, and a relation between local initializations and limiting consensus solutions is established, which is used to solve the least 2-norm solution.
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