On the Approximability of Budgeted Allocations and Improved Lower Bounds for Submodular Welfare Maximization and GAP

In this paper we consider the following maximum budgeted allocation (MBA) problem: Given a set of m indivisible items and n agents; each agent i willing to pay bij on item j and with a maximum budget of Bi, the goal is to allocate items to agents to maximize revenue. The problem naturally arises as auctioneer revenue maximization in budget-constrained auctions and as winner determination problem in combinatorial auctions when utilities of agents are budgeted-additive. Our main results are: • We give a 3/4-approximation algorithm for MBA improving upon the previous best of 0.632[AM04, Von08] (also implied by the result of [FV06]). Our techniques are based on a natural LP relaxation of MBA and our factor is optimal in the sense that it matches the integrality gap of the LP. • We prove it is NP-hard to approximate MBA to any factor better than 15/16, previously only NP-hardness was known [SS06, LLN01]. Our result also implies NP-hardness of approximating maximum submodular welfare wi...

• Type: Conference
• Year: 2008
• Where: FOCS
• Authors: Deeparnab Chakrabarty, Gagan Goel
• Keywords: Auctioneer Revenue Maximization, FOCS 2008, Maximum Budgeted Allocation, Theoretical Computer Science, Winner Determination Problem