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A 3D floor plan is a non-overlapping arrangement of blocks within a largebox. Floor planning is a central notion in chip-design, and with recentadvances in 3D integrated circuits, understanding 3D floor plans has becomeimportant. In this paper, we study so called mosaic 3D floor plans where theinterior blocks partition the host box under a topological equivalence. We giverepresentations which give an upper bound on the number of general 3D floorplans, and further consider the number of two layer mosaic floorplans. We provethat the number of two layer mosaic floor plans is $n^{(1+o(1))n/3}$. Thiscontrasts with previous work which has studied `corner free' mosaic floorplans, where the number is just exponential. The upper bound is by giving arepresentation, while the lower bound is a randomized construction.

Two Layer 3D Floor Planning