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The solution of linear least squares problems across large loosely connected distributed networks (such as wireless sensor networks) requires distributed algorithms which ideally need very little or no coordination between the nodes. We first provide an extensive overview of distributed least squares solvers appearing in the literature and classify them according to their communication patterns. We are particularly interested in truly distributed algorithms which do not require a fusion centre, cluster heads or any multi-hop communication. Beyond existing methods, we propose the novel least squares solver PSDLS, which utilises a recently developed distributed QR factorisation algorithm. All communication between nodes is exclusively performed within the push-sum algorithm for distributed aggregation.We analytically compare the communication cost of PSDLS and the existing truly distributed algorithms. In all these algorithms, the communication cost of reaching a predefined accuracy depends on many factors, including network topology, problem size, and settings of algorithm-specific parameters. We illustrate with simulation experiments that our novel PS-DLS solver requires significantly fewer messages per node than the previously existing methods to reach a predefined solution accuracy.

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