Abstract
In this paper, we compare six known linear distributed average consensus algorithms on a sensor network in terms of convergence time (and therefore, in terms of the number of transmissions required). The selected network topologies for the analysis (comparison) are the cycle and the path. Specifically, in the present paper, we compute closed-form expressions for the convergence time of four known deterministic algorithms and closed-form bounds for the convergence time of two known randomized algorithms on cycles and paths. Moreover, we also compute a closed-form expression for the convergence time of the fastest deterministic algorithm considered on grids.
Highlights
Since the number of transmissions per iteration on a grid of r rows and c columns is rc for the fastest linear time-invariant (LTI) distributed averaging algorithm for symmetric weights, the total number of transmissions required for τ e, W r,c 12 iterations is:
A cycle with the total number of transmissions required for τ e, W n 3 iterations is T e, W n 3
Since the number of transmissions per iteration ona path with n sensors is n for the total number of transmissions required for τ e, W n 3 iterations is T e, W n 3
Summary
A distributed averaging (or average consensus) algorithm obtains in each sensor the average (arithmetic mean) of the values measured by all the sensors of a sensor network in a distributed way. The most common distributed averaging algorithms are linear and iterative:. Is the value measured by the sensor v j , x j (t) is the value computed by the sensor v j in time t 6= 0 and the weighting matrix W (t) is an n × n real sparse matrix satisfying that if two sensors v j and vk are not connected (i.e., if v j and vk cannot interchange information), [W (t)] j,k = 0. The linear distributed averaging algorithms can be classified as deterministic or randomized depending on the nature of the weighting matrices W (t)
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