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Upper bounds on the communication complexity of finding the nearest latticepoint in a given lattice $\Lambda \subset \mathbb{R}^2$ was considered inearlier works~\cite{VB:2017}, for a two party, interactive communication model.Here we derive a lower bound on the communication complexity of a key step inthat procedure. Specifically, the problem considered is that of interactivelyfinding $\min(X_1,X_2)$, when $(X_1,X_2)$ is uniformly distributed on the unitsquare. A lower bound is derived on the single-shot interactive communicationcomplexity and shown to be tight. This is accomplished by characterizing theconstraints placed on the partition generated by an interactive code andexploiting a self similarity property of an optimal solution.

Towards a Converse for the Nearest Lattice Point Problem