Solving combinatorial exchanges: optimality via a few partial bids

We investigate the problem of matching buyers and sellers in a multi-item multi-unit combinatorial exchange so as to maximize either the surplus (revenue minus cost) or the trading volume (number of units traded). In such an exchange, participants can place bids to buy or sell bundles of goods. While even highly specialized cases of this problem are both NPComplete and inapproximable, we show that optimal surplus or trade volume can be achieved in polynomial time if some bids can be satisfied partially. Using theory of linear programming, we show that in exchanges trading multiple units of k distinct items, maximum surplus is possible with at most k partial bids, and maximum trade volume is possible with at most k + 1 partial bids. These bounds on the number of partial bids are the best possible in the worst case. For the simple but important case of single item exchanges, we also develop fast combinatorial algorithms for optimal matching. The bidding language that simply allows bidd...

• Type: Conference
• Year: 2003
• Where: SIGECOM
• Authors: Anshul Kothari, Tuomas Sandholm, Subhash Suri
• Keywords: Partial Bids, SIGECOM 2003, Single Item Exchanges, Trade Volume