The way i understand the steps

1. User visits the page and browser calls Parakeet service
2. Parakeet services generates C',S' parameters and calls multiple SSPs for each Interest Group. The SSPs then call multiple DSPs to collect ads with bids
3. Parakeet Service the does multiple round trips between itself, the same SSPs and DSPs it interacted in point 2 above to run secure multiple part computations for other quality controls as expected by sell side and buy side
4. Finally Parakeet service chooses the final ad and sends it back to the browser

We understand that caching techniques between SSPs, DSPs, Parakeet service could help but the network calls latency and multi party computations seem heavy even when done on server side.

Will love to understand how Parakeet team thinks about cutting latency which is critical