Before revision:  It is shown that the proposed cost functions are computationally efficient (only requires multiplication and square root calculation) and have several advantages over widely deployed constant product cost functions  .
After revision:  It is shown that the proposed cost functions are computationally efficient (only requires multiplication and square root calculation) and have several advantages over widely deployed constant product cost functions . For example, the proposed market makers are more robust against front-runner (slippage) attacks .