Approximation algorithms and online mechanisms for item pricing

We present approximation and online algorithms for a number of problems of pricing items for sale so as to maximize seller’s revenue in an unlimited supply setting. Our first result is an O(k)-approximation algorithm for pricing items to single-minded bidders who each want at most k items. This improves over recent independent work of Briest and Krysta [5] who achieve an O(k2 ) bound. For the case k = 2, where we obtain a 4-approximation, this can be viewed as the following graph vertex pricing problem: given a (multi) graph G with valuations we on the edges, find prices pi ≥ 0 for the vertices to maximize X {e=(i,j):we≥pi+pj } (pi + pj) . We also improve the approximation of Guruswami et al. [11] from O(log m + log n) to O(log n), where m is the number of bidders and n is the number of items, for the “highway problem” in which all desired subsets are intervals on a line. Our approximation algorithms can be fed into the generic reduction of Balcan et al. [2] to yield an in...

• Type: Conference
• Year: 2006
• Where: SIGECOM
• Authors: Maria-Florina Balcan, Avrim Blum
• Keywords: Algorithms, Et Al, Pricing Items, SIGECOM 2006