Parameterizing the winner determination problem for combinatorial auctions

Combinatorial auctions (CAs) have been studied by the multiagent systems community for some time, since these auctions are an effective mechanism for resource allocation when agents are self-interested. One challenge, however, is that the winner-determination problem (WDP) for combinatorial auctions is NP-hard in the general case. However, there are ways to leverage meaningful structure in the auction so as to achieve a polynomial-time algorithm for the WDP. In this paper, using the formal scope of parameterized complexity theory, we systematically investigate alternative parameterizations of the bids made by the agents (i.e. the input to the WDP for combinatorial auctions) and are able to determine when a parameterization reduces the complexity of the WDP (fixed-parameter tractable), and when a particular parameterization results in the WDP remaining hard (fixedparameter intractable). Our results are relevant to auction designers since they provide information as to what types of bidding-restrictions are effective for simplifying the winner determination problem, and which would simply limit the expressiveness of the agents while not providing any additional computational gains.