Computational Aspects of Clearing Continuous Call Double Auctions with Assignment Constraints and Indivisible Demand

We investigate the computational complexity of clearing markets in a continuous call double auction. In the simplest case, when any part of any bid can be matched with any part of any ask, the market can be cleared optimally in log-linear time. We present two generalizations, motivated by electronic marketplaces for the process industry, where: (a) there exist assignment constraints on which bids can be matched with which asks; and (b) where demand is indivisible. We show that clearing markets with assignment constraints can be solved efficiently using network flow algorithms. However clearing markets with indivisible demand, with or without assignment constraints, requires solving NP-hard optimization problems such as the generalized assignment problem, the multiple knapsack problem and the bin packing problem.