The Combinatorial Public Projects Problem (CPPP) is an abstraction of resource allocation problems in which agents have preferences over alternatives, and an outcome that is to be collectively shared by the agents is chosen so as to maximize the social welfare. We explore CPPP from both computational and mechanism design perspectives. We examine CPPP in the hierarchy of complement-free (subad-ditive) valuation classes and present positive and negative results for both unrestricted and truthful algorithms.
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