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The authors consider the remote computation of a function of two sources where one is receiver side information. Specifically, given side information Y, they wish to compute f(X, Y) based on information transmitted by X over a noise-less channel. The goal is to characterize the minimal rate at which X must transmit information to enable the computation of the function f. They establish that a minimum (conditional) entropy coloring of the product of characteristic graphs is asymptotically equal to the conditional graph entropy. This can be seen as a generalization of a result of Korner (1973) which shows that the minimum entropy coloring of product graphs is asymptotically equal to the graph entropy.
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