Abstract: An automated trading system, comprising an interface for receiving a plurality of orders comprising bid orders and ask orders; and a trading module for matching the bid orders and the ask orders, the trading module comprising a memory for storing the plurality of orders, a subset sum module configured to find the subset sums of the bid orders and the subset sums of the ask orders of the plurality of orders; and an order matching module for matching a combination of bid orders to a combination of ask orders based on the subset sums for the bid orders and the subset sums of the ask orders, wherein the subset sum module is configured to find the subset sums of a set of orders by considering a first set of orders, determining the subset sums of the first set of orders, considering a second set of orders wherein the second set of orders comprises at least one more order than the first set of orders and determining the subset sums of the second set of orders by using the determined subset suns of the first set of o

Abstract: The disclosure relates to an automated trading system, comprising an interface for receiving a plurality of orders comprising bid orders and ask orders and a trading module for matching the bid orders and the ask orders, the trading module comprising a memory for storing the plurality of orders, a subset sum module configured to find the subset sums of the bid orders and the subset sums of the ask orders of the plurality of orders, and an order matching module for matching a combination of bid orders to a combination of ask orders based on the subset sums for the bid orders and the subset sums of the ask orders.