Rent's Rule Estimate of Wire Length

If we know the physical area of each leaf cell we can estimate the area of each component in a heirarchic design (sum of parts plus percentage swell).

Rent's rule pertains to the organization of computing logic, specifically the relationship between the number of external signal connections to a logic block with the number of logic gates in the logic block, and has been applied to circuits ranging from small digital circuits to mainframe computers »[Wikipedia].

Rent gives a simple power-law relationship for the number of wires to a logic block. Wire length distribution (with good placement) follows an equally-predictable pattern.

With a heirarchic design, where we have the area use of each leaf cell, even without placement, we can follow a net's trajectorary up and down the hierarchy and apply Rent's Rule.

Hence we can estimate a signal's length by sampling a power law distribution whose 'maximum' is the square root of the area of the lowest-common-parent component in the hierarchy.

Illustrating Lowest Common Parent of the endpoint logic blocks. (This will always be roughly the same size for any sensible layout, so having a detailed layout like the one shown is not required).