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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This document was uploaded on 03/20/2014 for the course EECS 6.896 at MIT.

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