E.F. Rent's Discovery and First Publications
In the 1960s, E.F. Rent, an IBM employee, found a remarkable trend between the number of pins (terminals T) at the boundaries of integrated circuit designs at IBM and the number of internal components (g), such as logic gates or standard cells. On a plot, these datapoints were on a straight line, implying a power-law relation where t and p are constants (, and generally ). Rent disclosed his findings in IBM-internal memoranda that were published in the IBM Journal of Research and Development in 2005 (IBM J. Res. & Dev. Vol. 49, No. 4/5 July/September 2005, pp. 777–803), but the relation was described in 1971 by Landman and Russo. They performed a hierarchical circuit partitioning in such a way that at each hierarchical level (top-down) the least number of interconnections had to be cut to partition the circuit (in more or less equal parts). At each partitioning step, they noted the number of terminals and the number of components in each partition and then partitioned the sub-partitions further. They found the power law rule applied to the resulting T versus g plot and named it "Rent's rule". It is crucial to recognise that Rent's rule is an empirical result based on observations of existing designs, and therefore it is less applicable to the analysis of non-traditional circuit architectures. Having said that, it does provide a useful framework with which to compare similar architectures.
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