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In this work, we consider the problem of distributed computing of functionsof structured sources, focusing on the classical setting of two correlatedsources and one user that seeks the outcome of the function while benefitingfrom low-rate side information provided by a helper node. Focusing on the casewhere the sources are jointly distributed according to a very general mixturemodel, we here provide an achievable coding scheme that manages tosubstantially reduce the communication cost of distributed computing byexploiting the nature of the joint distribution of the sources, the sideinformation, as well as the symmetry enjoyed by the desired functions. Ourscheme -- which can readily apply in a variety of real-life scenarios includinglearning, combinatorics, and graph neural network applications -- is here shownto provide substantial reductions in the communication costs, whilesimultaneously providing computational savings by reducing the exponentialcomplexity of joint decoding techniques to a complexity that is merely linear.

Distributed Computing of Functions of Structured Sources with Helper Side Information