Combinatorial auctions are auctions in which each bid can be placed on a set of items, as opposed to standard auctions, in which each bid is placed on a single item. The winner determination problem for combinatorial auctions is known to be NP-complete. One of the approaches to cope with the hardness of the problem is to identify tractable classes of combinatorial auctions by means of hypertree decompositions. The winner determination problem is tractable on the class of instances with corresponding dual hypergraphs having hypertree width bounded by a fixed natural number. This book describes an optimal algorithm, called ComputeSetPackingK, for solving the winner determination problem based on these ideas. The algorithm was implemented, and experimental results are also presented.