problemset9 solutions

show that the minimum dimension of any layout of a

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Unformatted text preview: relying on what we did in class, but similar example, a leaf is a subtree of size . A node with two leaves as children is the root of subtree with size . � � ��� � � Handout 19: Solution Set 9 3 � Using Lemma 6, we can cut a binary tree exactly in half by cutting at most �� edges. For example, in the first cut, we ask for a subtree of size �. In the worst case, we only get a subtree of size �, and we still need to cut off � nodes. Thus, we ask for a subtree of size � on the next iteration and may be unlucky again, getting a subtree of size �. In the worst case, our cuts produce subtrees of size � �� � � �� � � ��� � , requiring �� cuts to cut the tree exactly in half. �� �� �� �� �� �� �� �� � �� � Problem 9-4. Show that there is a layout for cube-connected-cycles network (or a butterfly) with with only � � ���� � area. ��� � � � �� � vertices Solution: We proved th...
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