Explain the properties of hypercube, Computer Engineering

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Q. Explain the properties of Hypercube?

Properties of Hypercube:

Hypercube is both edge and node symmetric.
The labels of any two neighbouring nodes vary in exactly 1 bit.
A node p in n-cube has a unique label and binary ID which is n-bit binary number.
2 nodes whose labels vary in k bits are linked by a shortest path of length k.

Hypercube structure is able to employ many parallel algorithms requiring all-to-all communication which is algorithms in that every task should communicate with every other task. This arrangement allows a computation needing all-to-all communication amongst P tasks to be executed in only log P steps compared to polynomial time employing other data structures such as linked lists and arrays.

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