hw5-sp11 - !"! & # !$ ! '" # $ "( 1. (10...

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Unformatted text preview: !"! & # !$ ! '" # $ "( 1. (10 points) Considers n nodes numbered 1 through n, each holding a k-bit value. Node 1 wants to find the parity of the n*k bits collectively held by the n nodes. One solution for this will be for node 1 to obtain the k-bit values from nodes 2 through n, and then compute the parity. This will require (n-1)k bits of communication. Suggest a more efficient algorithm. What is the worst-case communication complexity (in bits) using your algorithm? Recommended Exercise: Consider 2 nodes A and B, each holding a k-bit value, the values being chosen uniformly at random from all possible k-bit values. Suppose that the two nodes want to determine whether their values are equal. Suggest an algorithm for this, and determine the average communication cost for your algorithm. ! # " $ & ! $ ' ( + $ $ * % $ $ ) ( * , + + ! , %, + %, , $ %% %% - ! . * ! " . ) ! ) ! / . + , ! , + %, *+ , %1 , + , 0, + , 0, 2 $ ' 34 34 ' # $ ! 4 $ ! /& ! ! ! 0 " ! # 5 2 . - 6 ! 0 )# . ! 6 0 . ) , -, 0, !+ + 7 ! ! & 0 ! ! . ) ! ! , ) 66 - 8 2 * 9 - $ : ! * % # * ! ; ! ! ' . ' ' - 4 ' ' ' - 0 ! ! $ !/ ! > 3 3 81 * ! $ = / $ 2 ) * - ) < ' * % ! ! 80 ! $0 $0 ...
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This note was uploaded on 02/08/2012 for the course ECE 428 taught by Professor Hu during the Spring '08 term at University of Illinois, Urbana Champaign.

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