Polkadot Block Production: SAFROLE
SAFROLE (formerly known as SASSAFRAS) is a SNARK-based block production algorithm that provides anonymity in the validator selection process. SAFROLE also aims to deliver (nearly) fork-free, constant time block production. SAFROLE is an upgrade to BABE, the block production portion of the hybrid consensus model that Polkadot uses (and later JAM).
zkSNARKs, in conjunction with a RingVRF, are used to ensure that slots are not preassigned to malicious actors that are not part of the active validator set. Using a zkSNARK would allow anonymity to be preserved when a validator submits a ticket, proving they are in the active set without revealing their identity. This solution enables a validator to prove they are part of an eligible group (via the RingVRF) while preserving anonymity within the block production mechanism and preventing the likelihood of spam.
Part of how SAFROLE minimizes the possibility of forks is by limiting the possibility of multiple valid authors per six-second timeslot (the time to produce a block) where a valid, possible author must only be a single key-holder from within a pre-specified group of validators. In other words, it limits the possibility of two heads of the chain (built on the same parent) forming. More on how SAFROLE prevents forks can be found in Section 4.3, 4.8, and 6 of the JAM Graypaper.