Automatic cell placement for quantum-dot cellular automata

Quantum-dot cellular automata (QCA) is a novel nano-scale computing mechanism that can represent binary information based on spatial distribution of electron charge configuration in chemical molecules. In this paper we develop the first cell-level placement of QCA circuits under buildability constraints. We formulate the QCA cell placement as a unidirectional geometric embedding of k-layered bipartite graphs. We then present an analytical and a stochastic solution for minimizing the wire crossings and wire length in these placement solutions.