OPTIMAL ALLOCATION PROBLEM WITH QUADRATIC UTILITY FUNCTIONS AND ITS RELATIONSHIP WITH GRAPH CUT PROBLEM

Akiyoshi Shioura, Shunya Suzuki
2012 Journal of the Operations Research Society of Japan  
We discuss the optimal allocation problem in combinatorial auctions, where the items are allocated to bidders so that the sum of the bidders' utilities is maximized, In this paper, we consider the case where utility functions are glven by quadratic functions; the class of such utility functions has a succinct representation but is suMciently general. The main airn of this paper is to show the computational complexlty of the optimal allocation problem with quadratic utility functions, We
more » ... the cases where utility functions are submodular and supermodular, and show NP-hardness andlor polynomial-time exact/approximation algorithrrrs, These results are given by using the relationship with graph cut problems such as the minlmax cut problem and the multiwabF cut problem.
doi:10.15807/jorsj.55.92 fatcat:bgcszeb4vjdtxfh7n7m2znrh2y