  We consider the problem of distributed computation of the nearest lattice
point for a two dimensional lattice. An interactive model of communication is
considered. We address the problem of reconfiguring a specific rectangular
partition, a nearest plane, or Babai, partition, into the Voronoi partition.
Expressions are derived for the error probability as a function of the total
number of communicated bits. With an infinite number of allowed communication
rounds, the average cost of achieving zero error probability is shown to be
finite. For the interactive model, with a single round of communication,
expressions are obtained for the error probability as a function of the bits
exchanged. We observe that the error exponent depends on the lattice.
