Exploring constant function market maker designs

A central limit order book (CLOB) is traditionally the most popular exchange methodology. Market makers submit their orders in the order book and wait for them to be accepted by order takers. The exchanges are responsible for aggregating orders, matching and executing them whenever buy and sell orders overlap. 

However, CLOBs are difficult to implement on-chain in a fully decentralized fashion due to the storage constraint of a blockchain. For an individual market pair, a decentralized exchange (DEX) would need to keep track of the amount of liquidity at every tick on-chain.