Consider the Omega network and Butterfly network from p nodes in the leftmost column to p nodes in the rightmost column for some p=2^k. The Omega network is defined in Chapter 2 of the text book such that Si is connected to element S j if j=2i for or j=2i+1-p for  See Chapter 2 in text book for its definition.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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  1. Consider the Omega network and Butterfly network from p nodes in the leftmost column to p nodes in the rightmost column for some p=2^k. The Omega network is defined in Chapter 2 of the text book such that Si is connected to element S j if j=2i for or j=2i+1-p for  See Chapter 2 in text book for its definition.

 

The Butterfly network is an interconnection network composed of log p

levels (as the omega network). In a Butterfly network, each switching node i at a level l is

connected to the identically numbered element at level l + 1 and to a switching node

whose number differs from itself only at the lth most significant bit. Therefore, switching

node Si is connected to element S j at level l if j = i or j .

 

  1. Prove that for each node Si in the leftmost column and a node Sj in the rightmost column, there is a path from Si to Sj in the Omega network.

 

  1. Prove that for each node Si in the leftmost and a node Sj in the rightmost, there is a path from Si to Sj in the Butterfly network.
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