Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
An o(n^3)-Time Algorithm Maximun-Flow Algorithm
SIAM Journal on Computing
Truth revelation in approximately efficient combinatorial auctions
Proceedings of the 1st ACM conference on Electronic commerce
Algorithm for optimal winner determination in combinatorial auctions
Artificial Intelligence
Improved Rounding Techniques for the MAX 2-SAT and MAX DI-CUT Problems
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Note on Kelso and Crawford's Gross Substitutes Condition
Mathematics of Operations Research
Optimal Inapproximability Results for Max-Cut and Other 2-Variable CSPs?
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Combinatorial Auctions
Optimal approximation for the submodular welfare problem in the value oracle model
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Tight information-theoretic lower bounds for welfare maximization in combinatorial auctions
Proceedings of the 9th ACM conference on Electronic commerce
Combinatorial auctions with k-wise dependent valuations
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Approximation algorithms for graph homomorphism problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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We discuss the optimal allocation problem in combinatorial auction, 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 given by quadratic functions; the class of quadratic utility functions has a succinct representation but is sufficiently general. The main aim of this paper is to show the 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 exact/approximation algorithm. These results are given by using the relationship with graph cut problems such as the min/max cut problem and the multiway cut problem.