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problemset9 solutions

Initially and there is just one size a power of two so

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Unformatted text preview: e following lemma in class on April 14. � Lemma 7There is a layout for an -input butterfy with only ��� � � area. Now, we show the following corollary, which is just a rewrite of the above lemma. Corollary 8There is a layout for a cube-connected-cycles network (or butterfly) with � � � ��� � area. ��� � �� � � � � � �� � vertices with only � � � inputs. So, applying Lemma 7, there is a Proof. A butterfly with � � � vertices is a butterfly with � � � ���� �� � space. We also have that �� � �� � , or � �� � �� . Since layout that takes � , we have � ���� � �� �� �. Thus, we have that the area is ��� �� ��� ��  �� � � �����  ��� ��  �� �, which reduces to � � � ...
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