This paper concerns the efficient construction of sparse and low stretch spanners for unweighted arbitrary graphs with n nodes. All previous deterministic distributed algorithms, for constant stretch spanners of o(n(2...
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This paper concerns the efficient construction of sparse and low stretch spanners for unweighted arbitrary graphs with n nodes. All previous deterministic distributed algorithms, for constant stretch spanners of o(n(2)) edges, have a running time Omega(n(epsilon)) for some constant epsilon > 0 depending on the stretch. Our deterministic distributed algorithms construct constant stretch spanners of o(n(2)) edges in o(n(epsilon)) time for any constant epsilon > 0. More precisely, in Linial's free model a.k.a LOCAL model, we construct in n(O(1/root log n)) time, for every graph, a (3, 2)-spanner of O(n(3/2)) edges, i.e., a spanning subgraph in which the distance is at most 3 times the distance of the original graph plus 2. The result is extended to (alpha(k), beta(k))-spanners with O(n(1+1/k) log k) edges for every integer parameter k >= 1, where alpha(k)+beta(k) = O(k(log25)). If the minimum degree of the graph is Omega(root n), then, in the same time complexity, a (5, 4)-spanner with O (n) edges can be constructed. (C) 2008 Elsevier B.V. All rights reserved.
distributed algorithms are gaining increasing research interests in the area of power system optimization and dispatch. Existing distributed power dispatch algorithms (DPDAs) usually assume that suppliers/consumers bi...
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distributed algorithms are gaining increasing research interests in the area of power system optimization and dispatch. Existing distributed power dispatch algorithms (DPDAs) usually assume that suppliers/consumers bid truthfully. However, this article shows the need for DPDAs to consider strategic players and to take account of their behavior deviation from what the DPDAs expect. To address this, we propose a distributed strategy update algorithm (DSUA) on top of a DPDA. The DSUA considers strategic suppliers who optimize their bids in a DPDA, using only the information accessible from a DPDA, that is, price. The DSUA also considers the cases when suppliers update bids alternately or simultaneously. Under both cases, we show the closeness of supplier bids to the Nash equilibrium via game-theoretic analysis as well as simulation.
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.
We design and analyze a fully distributed algorithm for convex constrained optimization in networks without any consistent naming infrastructure. The algorithm produces an approximately feasible and near-optimal solut...
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We design and analyze a fully distributed algorithm for convex constrained optimization in networks without any consistent naming infrastructure. The algorithm produces an approximately feasible and near-optimal solution in time polynomial in the network size, the inverse of the permitted error, and a measure of curvature variation in the dual optimization problem. It blends, in a novel way, gossip-based information spreading, iterative gradient ascent, and the barrier method from the design of interior-point algorithms.
Principal component analysis (PCA) is a fundamental primitive of many data analysis, array processing, and machine learning methods. In applications where extremely large arrays of data are involved, particularly in d...
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Principal component analysis (PCA) is a fundamental primitive of many data analysis, array processing, and machine learning methods. In applications where extremely large arrays of data are involved, particularly in distributed data acquisition systems, distributed PCA algorithms can harness local communications and network connectivity to overcome the need of communicating and accessing the entire array locally. A key feature of distributed PCA algorithm is that they defy the conventional notion that the first step toward computing the principal vectors is to form a sample covariance. This paper is a survey of the methodologies to perform distributed PCA on different data sets, their performance, and of their applications in the context of distributed data acquisition systems.
We study algorithms in the LOCAL model that produce secured output. Specifically, each vertex computes its part in the output, the entire output is correct, but each vertex cannot discover the output of other vertices...
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We study algorithms in the LOCAL model that produce secured output. Specifically, each vertex computes its part in the output, the entire output is correct, but each vertex cannot discover the output of other vertices, with a certain probability. As the extensive research in the distributed algorithms field yielded efficient decentralized algorithms, the discussion about the security of distributed algorithms was somewhat neglected. Nevertheless, many protocols and algorithms were devised in the research area of secure multi-party computation problem. However, the focus in those protocols was to work for every function f at the expense of increasing the round complexity, or the necessity of several computational assumptions. We present a novel approach, which identifies and develops those algorithms that are inherently secure (which means they do not require any further constructions). This approach yields efficient secure algorithms for various labeling and decomposition problems without requiring any hardness assumption, but only a private randomness generator in each vertex.(c) 2022 Elsevier Inc. 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.
Following the wide investigation in distributed computing issues by mobile entities of the last two decades, we consider the need of a structured methodology to tackle the arisen problems. The aim is to simplify both ...
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Following the wide investigation in distributed computing issues by mobile entities of the last two decades, we consider the need of a structured methodology to tackle the arisen problems. The aim is to simplify both the design of the resolution algorithms and the writing of the required correctness proofs. We would encourage the usage of a common framework in order to help both algorithm designers and reviewers in the intricate work of delivering and analyzing the proposed resolution strategies. We demonstrate the effectiveness and usefulness of the new methodology by highlighting various peculiarities arising in different scenarios. In particular, we consider two different tasks for asynchronous entities moving in the Euclidean plane and in graphs, respectively. We show how two resolution strategies have been designed by following the accurate guide dictated by the methodology. Furthermore, we also show how the corresponding correctness proofs are obtained. (c) 2021 Elsevier Inc. All rights reserved.
The development of distributed algorithms and, more generally, distributed systems, is a complex, delicate and challenging process. Refinement techniques of (system) models improve the process by using a proof assista...
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The development of distributed algorithms and, more generally, distributed systems, is a complex, delicate and challenging process. Refinement techniques of (system) models improve the process by using a proof assistant, and by applying a design methodology aimed at starting from the most abstract model and leading, in an incremental way, to the most concrete model, for producing a distributed solution. We show, using the distributed reference counting (DRC) problem as our study, how models can be produced in an elegant and progressive way, thanks to the refinement and how the final distributed algorithm is built starting from these models. The development is carried out within the framework of the event B method and models are validated with a proof assistant. (C) 2006 Elsevier B.V. All rights reserved.
We determine the call blocking performance of channel-allocation algorithms where every channel is available for use in every cell and where decisions are made by mobiles/portables based only on local observations. Us...
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We determine the call blocking performance of channel-allocation algorithms where every channel is available for use in every cell and where decisions are made by mobiles/portables based only on local observations. Using a novel Erlang-B approximation method, together with simulation, we demonstrate that even the simplest algorithm, the timid, compares favorably with impractical, centrally administered fixed channel allocation. Our results suggest that an aggressive algorithm, that is, one requiring call reconfigurations, could provide a substantially reduced blocking probability. We also present some algorithms which take major steps toward achieving the excellent blocking performance of the hypothetical aggressive algorithm but having the stability of the timid algorithm.
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