Hypercube Interconnection

Another static interconnection scheme

A k-dimensional hypercube
    contains 2^k processors (nodes)

Each processing node contains a switch

Below are examples of hypercubes of dimension 0 through 3
    The dotted edges shown where the hypercube
        is being extending from the next lower dimension hypercube

The nodes are numbered from 0 to 2^k - 1,
    usually in binary

Two nodes are separated by a single link
    if the binary values of their numbers
        differ by one bit
    E.g. node 000 is only one hop from node 010
        and node 000 is two hops from node 011
            (by path 000 -> 001 -> 011
              or by path 000 -> 010 -> 011)

Examining the figure above, notice

• The bottom plane contains all nodes numbered 3 and below
• The top plane contains all nodes numbered 4 and above
• The left plane contains all even-numbered nodes
• The right plane contains all odd-numbered nodes

What is the difference between the front and back planes?

Below is a hypercube of dimension 4:

Examples:

• Intel Hypercube

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Comments:
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