Omega network: Difference between revisions

An 8x8 Omega network is a multistage interconnection network, meaning that processing elements (PEs) are connected using multiple stages of switches. Inputs and outputs are given addresses as shown in the figure. The outputs from each stage are connected to the inputs of the next stage using a [[Faro shuffle|perfect shuffle]] connection system. This means that the connections at each stage represent the movement of a deck of cards divided into 2 equal decks and then shuffled together, with each card from one deck alternating with the corresponding card from the other deck. In terms of binary representation of the PEs, each stage of the perfect shuffle can be thought of as a cyclic [[Logical shift|logical left shift]]; each bit in the address is shifted once to the left, with the most significant bit moving to the least significant bit.

At each stage, adjacent pairs of inputs are connected to a simple exchange element, which can be set either straight (pass inputs directly through to outputs) or crossed (send top input to bottom output, and vice versa). For N processing element, an Omega network contains N/2 switches at each stage, and log₂N stages. The manner in which these switches are set determines the connection paths available in the network at any given time. Two such methods are destination-tag routing and XOR-tag routing, discussed in detail below.

For example, if a message's destination is PE 001, the switch settings are: upper, upper, lower. If a message's destination is PE 101, the switch settings are: lower, upper, lower. These switch settings hold regardless of the PE sending the message.

In XOR-tag routing, switch settings are based on (source PE) XOR (destination PE). This XOR-tag contains 1s in the bit positions that must be swapped and 0s in the bit positions that both source and destination have in common. The most significant bit of the XOR-tag is used to select the setting of the switch in the first stage; if the most significant bit is 0, the switch is set to pass-through, and if it is 1, the switch is crossed. The next-most significant bit of the tag is used to set the switch in the next stage, and so on until the final output has been selected.

In [[Multiprocessing#MIMD multiprocessing|multiprocessing]], omega networks may be used as connectors between the [|CPU|central[Central processing unit|CPU]]<nowiki/>s (CPUs) and their [[Shared memory (interprocess communication)#In hardware|shared memory]], in order to decrease the probability that the ''CPU-to-memory'' connection becomes a bottleneck.

* [https://github.com/vijendra/Omega-network Omega network simulation in c]