Hypercube network and properties, Computer Networking

Hypercube Network

The hypercube architecture has played a vital role in the development of parallel processing and is still not much popular and influential. The highly symmetric recursive structure of the hypercube supports several of elegant and efficient parallel algorithms. Hypercubes are also known as n-cubes, where n shows the number of dimensions. An- cube can be defined recursively as depicted below:

864_cube.png

                           3-cube built of 2 2-cubes

                                         193_4 cube.png

4-cube built of 2 3-cubes

 Properties of Hypercube:

  • A node p in a n-cube has a distinctive label, its binary ID, that is a n-bit binary number.
  • The labels of any two neighboring nodes vary in exactly 1 bit.
  • Two nodes whose labels vary in k bits are linked by a shortest path of length k.
  • Hypercube is both edge- symmetric and node.

Hypercube structure can be used to execute many parallel algorithms requiring all-to- all communication, that is, algorithms in which every task must communicate with every other task. This structure let a computation requiring all-to-all communication among P tasks to be performed in just log P steps compared t polynomial time using other data structures like linked lists and arrays.

Posted Date: 3/2/2013 7:41:15 AM | Location : United States







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