On the Approximability of Budget Feasible Mechanisms

Abstract

Previous chapter Next chapter Full AccessProceedings Proceedings of the 2011 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)On the Approximability of Budget Feasible MechanismsNing Chen, Nick Gravin, and Pinyan LuNing Chen, Nick Gravin, and Pinyan Lupp.685 - 699Chapter DOI:https://doi.org/10.1137/1.9781611973082.54PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract Budget feasible mechanisms, recently initiated by Singer (FOCS 2010), extend algorithmic mechanism design problems to a realistic setting with a budget constraint. We consider the problem of designing truthful budget feasible mechanisms for monotone submodular functions: We give a randomized mechanism with an approximation ratio of 7.91 (improving on the previous best-known result 233.83), and a deterministic mechanism with an approximation ratio of 8.34. We also study the knapsack problem, which is a special submodular function, give a 2 + √2 approximation deterministic mechanism (improving on the previous best-known result 5), and a 3 approximation randomized mechanism. We provide similar results for an extended knapsack problem with heterogeneous items, where items are divided into groups and one can pick at most one item from each group. Finally we show a lower bound of 1 + √2 for the approximation ratio of deterministic mechanisms and 2 for randomized mechanisms for knapsack, as well as the general monotone submodular functions. Our lower bounds are unconditional, and do not rely on any computational or complexity assumptions. Previous chapter Next chapter RelatedDetails Published:2011ISBN:978-0-89871-993-2eISBN:978-1-61197-308-2 https://doi.org/10.1137/1.9781611973082Book Series Name:ProceedingsBook Code:PR138Book Pages:xviii-1788