Sorting networks costs and delay

Question

From what I read I could not figure out how the cost and delay are calculated.

• Cost: the number of sticks or compare-exchange blocks.
• Delay: the number of compare-exchanges in sequence.

I have posted my example bellow

Answer 1

From what I can see, your answer is correct.

Cost is the total number compare exchanges done in the sorting network. I believe here it's 28.

Delay is the number of stages that must be done in sequence, ie have data dependencies. In the example there is a delay of 13.

Why do we care about the difference? Cost represents the amount of work we have to do in a serial implementation however the benefit of using a sorting network is that many of the compare-exchanges can be done in parallel. When you have as much parallelism available as there are compare-exchanges in a single stage, you can calculate that stage concurrently.

In a perfectly parallel system, the latency of the algorithm is going to be related to the delay rather than the cost. In a completely serial system, the latency is going to be related to the cost rather than the delay.