1. What have the authors contributed in "Accelerated distributed average consensus via localized node state prediction" ?
In this paper, the authors propose the use of extrapolation methods in order to accelerate distributed linear iterations.. The authors focus on a special case of the proposed framework and derive the optimal mixing parameter.. Noting that the optimal mixing parameter requires knowledge about the eigenvalues of the arbitrary weight matrix, the authors present a bound on the optimal parameter requiring only local information, and prove the validity of the suboptimal solution in the practical cases by showing that its performance is close–to–optimal and it is feasible in practical scenarios.. Finally, the authors provide simulation results that demonstrate the validity and effectiveness of the proposed scheme.
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2. What have the authors stated for future works in "Accelerated distributed average consensus via localized node state prediction" ?
In this section the authors present the calculation of the probability that two randomly selected nodes in a sensor network with connectivity radius rc and sensors uniformly distributed pxi, yi ( xi, yi ) = 1, xi, yi ∈ [ 0, 1 ] in a normalized square area D such that D = { x, y|x, y ∈ [ 0, 1 ] } on the plane are connected.. As was mentioned before, this 25 probability can be evaluated using integral of the form p = ∫∫∫∫ S pxi, yi ( xi, yi ) pxj, yj ( xj, yj ) dxidyidxjdyj ( 128 ) where the set S is defined as follows S = { ( xi, yi, xj, yj ) | ( xi − xj ) 2 + ( yi − yj ) 2 ≤ r2c ; xi, yi, xj, yj ∈ [ 0, 1 ] } ( 129 ). To facilitate calculation of the integral ( 128 ) given the set of integration limits ( 129 ) the authors can divide this problem into two parts: rc ≤ 1 and 1 < rc ≤ √. Note also that random variables x and y can be introduced: x = xi − xj, y = yi − yj.
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