Two Layer 3D Floor Planning

Abstract

A 3D floorplan is a non-overlapping arrangement of blocks within a large box. Floor planning is a central notion in chip-design, and with recent advances in 3D integrated circuits, understanding 3D floorplans has become important. In this paper, we study so called mosaic 3D floorplans where the interior blocks partition the host box under a topological equivalence. We give representations which give an upper bound on the number of general 3D floorplans, and further consider the number of two layer mosaic floorplans. We prove that the number of two layer mosaic floorplans is $n^{(1+o(1))n/3}$. This contrasts with previous work which has studied 'corner free' mosaic floorplans, where the number is just exponential. The upper bound is by giving a representation, while the lower bound is a randomized construction.