On the Exact Reliability Enhancements of Small Hammock Networks

In this paper, we study small hammock networks, more precisely the 29 hammock networks presented by Moore and Shannon in their prescient paper from 1956, where this type of network was introduced. We will first of all review the concept of the reliability polynomial, and define hammock networks, and emphasize some of their properties. We will then review the state of the art from three different angles: theoretical, algorithmic, and design oriented. These will show that results obtained over many years advocate very strongly for the small hammock networks. Because array-based designs (e.g., FinFETs) seem to be a perfect fit for small hammocks (as are nanoelectromechanical systems or NEMS), we have decided to start investigating them closely. The analyses we pursue here are exact, the coefficients of the reliability polynomials being determined using our own program. The reliability polynomials for non-trivial hammock networks are reported here as functions of the probability (p) that the device is closed. As far as we know, this is the first time they have appeared in this form. Our purpose in determining exact results is a practical one, as we foresee that small hammock networks could play a key role in any array-based design. That is why their reliability enhancements are evaluated thoroughly, using both classical and non-standard cost functions. Finally, conclusions are followed by a longer list of future directions of research, some of them practical while others more theoretical.