Introduction to Omega Network

An Omega network is a network configuration often used in parallel computing architecturesOmega Network is a dynamic multistage interconnection network, which connects processors to memory or I/O. 

Properties

• An N-input omega network requires log₂N stages of 2 x 2 switches. 
• Each stage of this network is interconnected in the same manner.
• Each stage consists of  N/2 switch boxes. Each switch box is in any of the four states (i.e. straight, exchange, upper broadcast, or lower broadcast).
• There is perfect shuffle exchange interconnection between every adjacent stage.
• The interconnections between the stages in an Omega Network are defined by the “rotate left” of the bits.

000 -> 000 -> 000 -> 000
001 -> 010 -> 100 -> 001
010 -> 100 -> 001 -> 010
100 -> 001 -> 010 -> 100
011 -> 110 -> 101 -> 011
101 -> 011 -> 110 -> 101
110 -> 101 -> 011 -> 110
111 -> 111 -> 111 -> 111

• Omega network has the same “internal blocking problem” as the Delta network. And differs from the delta network in the pattern of interconnections between the stages.

Problems

• There are some permutations that cannot be established by the omega network, so it is a blocking network.
• Omega network has another problem called Path Contention. When two different pairs of source nodes try to create connections with different nodes and use the same connection path to transfer the data to respective destination nodes, Then this problem occurs.

Application

• This type of network is used as a connector between the CPUs and their shared memory.
• Omega Network is often used in parallel computing architectures. It is an indirect topology that relies on the perfect shuffle interconnection algorithm.