X*Y=K vs X+Y=K

NFT itself is far different from FT assets in number due to its non-fungible identity, so NFT AMM needs the most efficient matching algorithm. At present, Uniswap v3 algorithm is the most efficient liquidity utilization in the Defi field. The combination of Tick and $X*Y=K$. is adopted in Uniswap v3 algorithm to obtain high liquidity utilization efficiency. However, in the field of NFT, since NFT has no decimal places, it will be more complicated to continue to use $X*Y=K$. for calculation, and on top of the gas consumption of NFT itself, we need to optimize the AMM algorithm model under the framework of Uniswap v3. ​

$X+Y=K$.is a constant sum formula. In this AMM algorithm, X and Y can always be exchanged at a fixed exchange rate. Therefore, the computational complexity of this algorithm is very low and it is suitable for the calculation of special types of assets such as NFT. By combining the Tick of Uniswap v3 with $X+Y=K$., the liquidity utilization efficiency of Uniswap v3 can also be inherited and reduce the complexity of AMM algorithm itself as well. ​