  We show that the three-dimensional layers-of-maxima problem can be solved in
$o(n\log n)$ time in the word RAM model. Our algorithm runs in $O(n(\log \log
n)^3)$ deterministic time or $O(n(\log\log n)^2)$ expected time and uses O(n)
space. We also describe an algorithm that uses optimal O(n) space and solves
the three-dimensional layers-of-maxima problem in $O(n\log n)$ time in the
pointer machine model.
