## Combinatorial auctions: a surveyCenter for Mathematical Studies in Economics and Management Science, Northwestern University, 2000 - 47 pages |

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allocation approximation algorithms assigned auction scheme AUSM bid on combinations bidders submit bids bids submitted branch and bound branch and cut called CAP2 CAP3 cjXj column combinatorial auctions computational consecutive ones property constraint matrix CPLEX cutting plane decentralized distribution dual variables efficient example extended formulations extreme point solution feasible solution formulation CAP1 fractional solutions Fujishima incentive compatibility individual items instances of SPP integer program interpretation iteration j€N SCM Lagrangean relaxation lanes large number linear programming linear programming relaxation logarithmic scale methods Nemhauser and Wolsey non-linear prices NP-hard number of bids number of items objective function value OptiBid optimal auction optimal objective function optimal solution optimization problem Packing Problem partition polyhedron randomly restriction revenue Sandholm seller Set Covering Problem set of bids sets of objects solved in polynomial subgradient subsets of objects test problems valuations VCG scheme Walrasian auctioneer weighted random