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Unformatted text preview: s added due to the folds. Since the width of the circuit at the folds is
only , there can only be wires crossing the fold. Thus, we can ﬁt the circuit with the new wires inside a box that is
� � � � � �� � �1 , which ﬁts inside a square box with dimensions � � � � � � �� � � �. The
�
� � � �� � � � � � � � . Since
, we have that this area is less than
total area is thus less than �
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, and the total area of the circuit did not increase by more than the constant factor of �. �
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�� �� �� �� �� � �� � ��� �� � �� � Problem 92. Show that for any VLSI layout of a complete binary tree with all the leaves in a straight line, that the
total wire area is �� ��� �. �� Solution: � Lemma 2For any VLSI layout of a complete binary tree with leaves in a straight line, the wire area of the longest 2
roottoleaf path is at least � � �. �� Proof. This lemma is fairly o...
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This document was uploaded on 03/20/2014 for the course EECS 6.896 at MIT.
 Spring '07
 BradleyKuszmaul

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