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.
/lp/association-for-computing-machinery/combinatorial-auctions-with-tractable-winner-determination-tovx0G9l2L