The name is absent

increases, the correlation between their scaling factors decreases. Thus, far gates
might have totally different scaling factors. We should penalize solutions in which
nearby gates do not have close scaling factors.

â Consider optimization problem in Equation 3.5. We add a number of the
constraints to the optimization problem such that they enforce spatially correla-
tion solutions. Assume g_u and g_υ are two logic gates that are located at (x_u, y_u)
and (x_v, y_v), respectively. Similar to Section 3.2, their scaling factors are denoted
by φ_u and φ_υ. We use the following optimization problem to improve variation
estimation.

min∣∣Ad-p∣∣2+       7('⅛,∙_υ)(≠_u - ≠υ)²,             (3∙9)

where

d^,u,v — ∖/(ʃu        ÷ (.Ун Уу)%ɔ

£ ⁼ {(9u,9v)∖9u and g_υ are two gates in the circuit}, (3.10)

and 7(.) is a monotone-decreasing function. Thus, when the distance between
two gates (⅛_x,_υ) is small, 7(d_u,_υ) is large. It enforces a small value for (φ_υ — φ_υ)².
Consequently, when, the distance between two gates (d_u,υ) is large, 7(d_M>1,) is small
and (φ_u-φv}² dɑeɛ not affect optimization problem dramatically. Hence, solution
of the optimization problem in Equation 3.9 will exhibit spatial correlations.

To simplify the constraints, one can eliminate the gate pairs that are far from

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