Efficient Representation of Interconnection Length Distributions Using Generating Polynomials

A renewed interest in interconnection length distribution models leaves many researchers with the task of enumerating shortest distances between cells in a physical architecture. This enumeration process is cumbersome and timeconsuming. In this paper, we simplify it by representing interconnection length distributions by generating polynomials. We show that this representation greatly facilitates the enumeration, allows the early calculation of key distribution parameters and provides a very compact representation. We use the inherent symmetry in physical architectures to construct generating polynomials with the composition and convolution techniques. It is shown that the construction of the generating polynomials using these techniques is much simpler than the construction of the distribution itself. We also present an efficient way to extract the final distribution from its generating polynomial