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Multi-User Linearly-Separable Distributed Computing
  • Ali Khalesi ,
  • Petros Elia
Ali Khalesi
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Petros Elia
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Abstract

In this work, we explore the problem of multi-user linearly-separable distributed computation, where N servers help compute the desired functions (jobs) of K users, and where each desired function can be written as a linear combination of up to L (generally non-linear) subtasks (or sub-functions). Each server computes some of the subtasks, communicates a function of its computed outputs to some of the users, and then each user collects its received data to recover its desired function. We explore the computation and communication relationship between how many servers compute each subtask vs. how much data each user receives.
For a matrix F representing the linearly-separable form of the set of requested functions, our problem becomes equivalent to the open problem of sparse matrix factorization F=DE over finite fields, where a sparse decoding matrix D and encoding matrix E imply reduced communication and computation costs respectively. This paper establishes a novel relationship between our distributed computing problem, matrix factorization, syndrome decoding and covering codes. To reduce the computation cost, the above D is drawn from covering codes or from a here-introduced class of so-called ‘partial covering’ codes, whose study here yields computation cost results that we present.
Oct 2023Published in IEEE Transactions on Information Theory volume 69 issue 10 on pages 6314-6339. 10.1109/TIT.2023.3283967