Fractional Knapsack Problem

a polynomial-time solvable problem

In the Standard exchange, traders initiate their trading intentions by submitting orders, which can be in the form of limit orders or market orders. Orders are all continuous, and traders can match with the fraction of each order. Within this exchange, the heart of the trading process is a sophisticated matching engine implemented as a smart contract. This smart contract takes on the role of a solver, working tirelessly to optimize trading outcomes for participants. It accomplishes this by tackling a challenging problem akin to the fractional knapsack problem.

Just as in the fractional knapsack problem where you aim to maximize value while fitting items into a limited capacity knapsack by taking fractions of items, the matching engine employs a similar concept. It seeks to determine the most advantageous way to pair buyers and sellers, optimizing trade execution by considering various factors. These factors may include order prices, quantities, and available liquidity. The smart contract intelligently determines how to match orders to achieve the best possible outcome for all parties involved, all while adhering to the constraints and rules set by the exchange.

In essence, the Standard exchange's matching engine operates as a dynamic problem solver, continually evaluating and optimizing trade executions to provide traders with the most favorable results. This approach ensures that traders can efficiently and effectively execute their orders, maximizing their returns while contributing to the overall liquidity and efficiency of the exchange.