# Butterfly Networks

Good Essays
Topics: Trees, Tree, Graph theory
BUTTERFLY NETWORK

Butterfly network is a network with 2q nodes and q + 1 columns as an unfolded q-cube in order to facilitate the discussion, visualization, and analysis of hypercube routing algorithms. However, a butterfly network can be viewed as a parallel processing architecture in its own right. A butterfly architecture (Fig. A, left) has p = 2 q(q + 1) processors of maximum degree d = 4, a diameter of 2q = ∪(log p), and a bisection width of ( – 1)2 q+1 + 0(2 q) = ∪(p/log p). A wrapped butterfly architecture is obtained if we superimpose or merge the nodes in Columns 0 and q of an ordinary butterfly. The resulting network has p = 2 qq processors, a uniform node degree of 4, a diameter of roughly 1.5q, and a bisection width of 2 q . Each node in a butterfly can be identified by its row and column numbers (x , y), where 0 ≤ x < 2 q – 1 and 0 ≤ y ≤ q (q – 1 for wrapped butterfly). Node (x, y) of a butterfly is connected to the four nodes (x, y – 1 ), (x, y + 1), (N y –1(x), y – 1), and (Ny (x), y + 1), if they exist.

[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]

Figure (A) : Butterfly and wrapped butterfly networks.

In the case of wrapped butterfly, the expressions y ± 1 for the column numbers are evaluated modulo q. If you shift the columns of a butterfly network cyclically, or permute them in any way, you can redraw the figure (by exchanging rows) such that it looks exactly the same as before.
Figure (A) shows an example in which the connection pattern between Columns 0 and 1 has been interchanged with that between Columns 1 and 2. It is easily seen that if we redraw the network by interchanging the places of Rows 1 and 2 as well as Rows 5 and 6, the resulting diagram will look exactly like the left-hand diagram in Fig. (A). The butterfly network is quite versatile. Many other independently developed networks are in fact butterfly network in disguise. Take a fat tree, for example. Recall that a

## You May Also Find These Documents Helpful

• Powerful Essays

the butterfly summary by chuang tzu:- The butterfly:- Chuang Tzu, a contemporary of Mencius, is universally regarded as the greatest Taoist after Lao Tzu. His butterfly dream is probably the most celebrated dream ever to be recorded in the history of Chinese Philosophy, which makes it almost impossible to omit in any serious expositions of Chuang Tzu's works. Whether or not the dream actually occurred is not a matter of great importance. What is important is that it has captured the minds of…

• 1266 Words
• 6 Pages
Powerful Essays
• Powerful Essays

POETRY ANALYSIS- Andrew Ma Subject Poem- TO A Butterfly By William Wordsworth I've watched you now a full half-hour, Self-poised upon that yellow flower; And, little Butterfly! indeed I know not if you sleep or feed. How motionless!---not frozen seas 5 More motionless! and then What joy awaits you, when the breeze Hath found you out among the trees, And calls you forth again ! This plot of orchard-ground is ours; 10 My trees they are, my Sister's flowers; Here rest your wing when they…

• 1755 Words
• 8 Pages
Powerful Essays
• Good Essays

Butterflies are wonderful creatures. They can’t swim, but they sure are very very good at flying. They can fly for long long long long long distances and they are also good at eating and giving birth. They look beautiful. They used to be a creepy ant, but then they grew out of their “shell” and a beautiful butterfly cane out. Butterflies are spelt “”b u t t e r f l i e s”. There are tons of different types. “The Butterfly Website is the world's oldest and largest website dedicated to butterflies…

• 276 Words
• 2 Pages
Good Essays
• Good Essays

Butterflies For my project workshop essay I will be studying butterflies. I know it might sound boring but it’s actually not. Okay I’m lying, oh well. So in this assignment I will be mentioning things like the life cycle of a butterfly, what they eat, their body parts, and stuff like that. So let’s get started. Did you know that butterflies have one of the most dramatic life cycles of any insect member of the insect world? Well they do. The cycle begins when the adult female butterfly lays…

• 436 Words
• 2 Pages
Good Essays
• Good Essays

Butterfly Whenever I hear the word butterfly, the first word that will come to my mind is the word beautiful. Likewise,I think the best example for beautiful is butterfly. For me, they compromise each other just like how their sounds were alike. If I were to describe a butterfly physically, first thing I would notice aside from how beautiful it was is that it was also small and being small makes them cuter than ever. Another thing is thatthere are tons of different types. Butterfly comes in different…

• 1763 Words
• 8 Pages
Good Essays
• Good Essays

Natural butterfly habitats have been destroyed or affected by construction of housing and shopping developments, as well as by the use of pesticides and other chemicals. You can provide a suitable butterfly habitat that will help fortify the butterfly population, and as an added bonus, the habitat will bring you enjoyment in watching beautiful butterflies in your yard. The butterfly habitat should be relatively sunny (5-6 hours per day) and out of the wind. Butterflies can get their required nutrients…

• 267 Words
• 2 Pages
Good Essays
• Satisfactory Essays

Session 3: Case Study Covered Call and Butterfly Strategies B. Butterfly strategy 1. What is the Butterfly strategy? * A neutral option strategy combining bull and bear spreads. Butterfly spreads use four option contracts with the same expiration but three different strike prices to create a range of prices the strategy can profit from. 2. What are its advantages and disadvantages? * Large profit percentage due to low cost involve in executing the position Limited risk…

• 313 Words
• 2 Pages
Satisfactory Essays
• Good Essays

Butterflies and Moths For decades, the Dominican Republic was ruled under the dictatorship of Rafael Trujillo. His harsh ways destroyed the chance for freedom, equality, education, and happiness for the citizens. In the novel, In the Time of the Butterflies, by Julia Alvarez, the Mirabal sisters, Patria, Minerva, Dede, and Maria Teresa, politically take a stand in hope to fight for their country. They were Las Mariposas, “the butterflies,” the strong sisters of the face of rebellion and leadership…

• 686 Words
• 3 Pages
Good Essays
• Satisfactory Essays

Music 101 October 26, 2013 “Madama Butterfly” Madama Butterfly is a very tragic story of love and loss, devotion and betrayal. Anyone that has been betrayed by their lover can relate to this story. On a very large hill in Nagasaki, japan a very handsome lieutenant by the name of Pinkerton, is looking over a home he has recently rented from a real estate agent by the name of Goro. Goro is not only a real estate agent ,but also a marriage broker Goro has made sure that along with Pinkertons…

• 689 Words
• 3 Pages
Satisfactory Essays
• Satisfactory Essays

Geography 1 5/12/14 The Butterfly Effect The butterfly effect is a term that has made it's way into popular culture thanks to movies and television, but the true meaning of the term is based on actual science. From a technical standpoint, it refers to the sensitive dependence on initial conditions in chaos theory. This theory explains that tiny changes within a complex system, lead to results that are impossible to predict. The name “butterfly effect” was coined after the famous example…

• 546 Words
• 2 Pages
Satisfactory Essays