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Combinatorial auctions with tractable winner determination

Some recent advances in the identification of tractable classes of combinatorial auctions are discussed. In particular, the work of [Gottlob and Greco 2007] is illustrated, where a research question raised in [Conitzer et al. 2004] is solved by showing that the class of structured item graphs is not efficiently recognizable (i.e., deciding the membership of instances is NP-hard), and where this difficulty is overcome trough a different approach based on the notion of hypertree decomposition.