final solutions

A what is the asymptotic number of connections to the

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Unformatted text preview: er bound on � � �. � Solution: �� ��. Suppose a switch at level i is cut. There are �� inputs that can reach this switch and ���  � outputs. Routing from any such input to any such output will be impossible, but all other paths still exist(the butterfly has unique paths between any input and output). So if we either exclude these inputs or these outputs from from the set of m, we will be able to route everything. � max� min��� � ���  � � � � � � 6.896 Final Examination Name 9 Problem 5. Butterfly Fat-Tree (3 parts) [16 points] Consider a butterfly fat-tree in which every � out of � levels consist of butterfly switches and every � out of � levels consists of tree switches. (a) What is the asymptotic number of connections to the root of such an � -leaf fat-tree? Justify yo...
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