Frugality ratios and improved truthful mechanisms for vertex cover

In set-system auctions, there are several overlapping teams of agents, and a task that can be completed by any of these teams. The auctioneer's goal is to hire a team and pay as little as possible. Examples of this setting include shortest-path auctions and vertex-cover auctions. Recently, Karlin, Kempe and Tamir introduced a new definition of frugality ratio for this problem. Informally, the "frugality ratio" is the ratio of the total payment of a mechanism to a desired payment bound. The ratio captures the extent to which the mechanism overpays, relative to perceived fair cost in a truthful auction. In this paper, we propose a new truthful polynomial-time auction for the vertex cover problem and bound its frugality ratio. We show that the solution quality is with a constant factor of optimal and the frugality ratio is within a constant factor of the best possible worst-case bound; this is the first auction for this problem to have these properties. Moreover, we show h...

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Edith Elkind, Leslie Ann Goldberg, Paul W. Goldberg
• Keywords: Auctions, CORR 2006, Education, Frugality Ratio, Vertex-cover Auctions