is given by . Lower bounds on p depend on the interconnection topology, since it is generally impossible to make all wires short. This lower bound is often called the "intrinsic Rent exponent", a notion first introduced by Hagen et al. It can be used to characterize optimal placements and also measure the interconnection complexity of a circuit. Higher (intrinsic) Rent exponent values correspond to a higher topological complexity. One extreme example () is a long chain of logic blocks, while a clique has . In realistic 2D circuits, ranges from 0.5 for highly-regular circuits (such as SRAM) to 0.75 for random logic. System performance analysis tools such as BACPAC typically use Rent's rule to calculate expected wiring lengths and wiring demands. Rent's rule has been shown to apply among the regions of the brain of Drosophila, using synapses instead of gates, and neurons which extend both inside and outside the region as pins. Estimating Rent's exponent To estimate Rent's exponent, one can use top-down partitioning, as used in min-cut placement. For every partition, count the number of terminals connected to the partition and compare it to the number of logic blocks in the partition. Rent's exponent can then be found by fitting these datapoints on a log–log plot, resulting in an exponent p'''. For optimally partitioned circuits, but this is no longer the case for practical (heuristic) partitioning approaches. For partitioning-based placement algorithms . Region II of Rent's rule Landman and Russo found a deviation of Rent's rule near the "far end", i.e., for partitions with a large number of blocks, which is known as "Region II" of Rent's Rule. A similar deviation also exists for small partitions and has been found by Stroobandt, who called it "Region III". Rentian wirelength estimation Another IBM employee, Donath, discovered that Rent's rule can be used to estimate the average wirelength and the wirelength distribution in VLSI chips. This motivated the System Level Interconnect Prediction workshop, founded in 1999, and an entire community working on wirelength prediction (see a survey by Stroobandt). The resulting wirelength estimates have been improved significantly since then and are now used for "technology exploration". The use of Rent's rule allows to perform such estimates a priori'' (i.e., before actual placement) and thus predict the properties of future technologies (clock frequencies, number of routing layers needed, area, power) based on limited information about future circuits and technologies. A