Unformatted text preview: he longest roottoleaf path in � � . Let �� be the length of the longest roottoleaf path in � � . Let
� � � �� 3 �� � � �� the most unbalanced case, where �
� , we have a rectangle that is
. This is “nearly square”
because � , and hence � , so the longer dimension is at most times the shorter one.
2 ties are broken arbitrarily
3 The longest roottoleaf path has to pass through the roots of one of the subtrees, so it must include the roottoleaf path of one of the subtrees
1 in � � Handout 19: Solution Set 9 2 �� and �� be the total wire area of each of the subtrees � � and ��, respectively, not counting the longest roottoleaf
paths. Then the total wire area � of � not counting the longest roottoleaf path is given by � � � � � �� � �� . Since
�� and �� have ��� leaves, �� � ������, and �� � ������. Thus, � � �������...
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 Spring '07
 BradleyKuszmaul
 Graph Theory, vlsi layout

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