The present invention is systems and methods for matching desired purchases and sales of mis-matched items. These systems and methods compare the requirements of potential buyers and sellers of items against those of sets of other potential buyers and sellers of items to construct transaction sets that will enable an optimal transaction or set of transactions for the parties involved. The present invention may be used to match purchases and sales of any items, such as goods, services, financial instruments, and property interests (e.g., ownership interests in real property, possessory interests in personal property, etc.).