Addendum and Correction: I realized that the key data structure is not the same as a hyperoctree, which would not suffice to prove the main theorem.   It is the same in 1 dimension.  In 2 or more dimensions, it is essential to take the Cartesian product of the 1-dimensional tree structure, which yields a poset of dyadic boxes of all shapes, not just cubes.  This carefully considered data structure is somewhat similar to a hyperoctree and this perhaps can be mentioned.  However, the proof of and algorithm for the main theorem is even more original than I first realized.

[I had not meant to write another addendum, but this one is necessary to correct a mistake in my main referee report.]