Abstract
We discuss the optimal allocation problem in combinatorial auctions, where the items are al- located to bidders so that the sum of the bidders' utilities is maximized. In this paper, we consider the case where utility functions are given by quadratic functions; the class of such utility functions has a suc- cinct representation but is sufficiently general. The main aim of this paper is to showthe computational complexity of the optimal allocation problem with quadratic utility functions. We consider the cases where utility functions are submodular and supermodular, and show NP-hardness and/or polynomial-time ex- act/approximation algorithms. These results are given by using the relationship with graph cut problems such as the min/max cut problem and the multiway cut problem.
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