On the computational complexity of the maximum trade problem

Consider a computer assisted trading system in which the needs and the products of the traders are compared by a computer system and the trading proceeds without attaching a dollar price to each commodity. In such a system the computer serves as an “intelligent” communication link between traders, enhancing the ability of producers and consumers to exchange goods. In this paper, we examine one computational aspect of such computerized trading schemes: Given a list of trading proposals (each proposal specifying the quantities of the commodities to be traded), how should one arrange the trades so that the maximum number of trades can be made in the market? We show that this maximum trade problem is computationally hard; it is NP-complete (Nondeterministic Polynomial Time Complete). We then describe some related open questions and potential solutions.