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problemset9 solutions

# Thus we can t the circuit with the new wires inside a

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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 � �� �� �� , and the total area of the circuit did not increase by more than the constant factor of �. � � �� � �� � �� � �� �� �� �� �� � �� � ��� �� � �� � Problem 9-2. 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 root-to-leaf path is at least � � �. �� Proof. This lemma is fairly o...
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