Maximal empty cuboids among points and blocks

Given a three-dimensional box containing n points, we consider the problem of identifying all Maximal Empty Isothetic Cuboids (MEC), i.e., all 3D empty parallelepiped bounded by six isothetic rectangular faces. It is shown that the total number of MECs is bounded by O(n3) in the worst case. An output-sensitive algorithm, based on plane-sweep paradigm, is proposed for generating all the MECs present on the floor. The algorithm runs in O(C + n2logn) time in the worst case, and requires O(n) space, where C is the number of MECs present inside the box.