Average Interconnection Length and Interconnection Distribution Based on Rent´s Rule

In this paper we show that it is necessary to utilize different partitioning coefficients in interconnection length analyses which are based on Rent´s rule, depending on whether one- or two-dimensional placement strategies are used. β, the partitioning coefficient in the power-law relationship αβ^β, provides a measure of the number of interconnections which cross a boundary enclosing β blocks. The partitioning coefficients are β=ρ/2 and β=ρ for two- and one-dimensional arrays, respectively, where ρ is the experimental coefficient of the Rent relationship Τ=αβ^ρ. Based on these separate partitioning coefficients, an average interconnection length prediction is presented for rectangular arrays that outperforms existing predictions. Examples are given to support this theory.