Approximation Algorithms for Non-single-minded Profit-Maximization Problems with Limited Supply

We consider profit-maximization problems for combinatorial auctions with non-single minded valuation functions and limited supply. We obtain fairly general results that relate the approximability of the profit-maximization problem to that of the corresponding social-welfare-maximization (SWM) problem, which is the problem of finding an allocation (S1, . . . , Sn) satisfying the capacity constraints that has maximum total value j vj(Sj). Our results apply to both structured valuation classes, such as subadditive valuations, as well as arbitrary valuations. For subadditive valuations (and hence submodular, XOS valuations), we obtain a solution with profit OPTSWM /O(log cmax), where OPTSWM is the optimum social welfare and cmax is the maximum item-supply; thus, this yields an O(log cmax)-approximation for the profit-maximization problem. Furthermore, given any class of valuation functions, if the SWM problem for this valuation class has an LP-relaxation (of a certain form) and an algorith...

• Type: Journal
• Year: 2010
• Where: WINE
• Authors: Khaled M. Elbassioni, Mahmoud Fouz, Chaitanya Swamy
• Keywords: Arbitrary Valuations, Cmax, Economy, Profit-maximization Problem, WINE 2010