Frugality ratios and improved truthful mechanisms for vertex cover Export

@misc{citeulike:1001111, abstract = {In {\em set-system auctions}, there is a task than can be completed by several overlapping teams of selfish agents, and the centre's goal is to hire one of these teams 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 {\em 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. We bound its frugality ratio. We show that both the solution quality and the frugality ratio of our auction are within a constant factor of optimal; this is the first auction for this problem to have these properties. Moreover, we show how to transform any truthful auction into a frugal one while preserving the approximation ratio. Also, we consider two natural modifications of the definition of Karlin et al., and we analyse the properties of the resulting payment bounds, such as monotonicity, computational hardness, and robustness with respect to the draw-resolution rule. We study the relationships between the different payment bounds, both for general set systems and for specific set-system auctions, such as path auctions and vertex-cover auctions. We use these new definitions in the proof of our main result for vertex-cover auctions via a bootstrapping technique, which may be of independent interest.}, archivePrefix = {arXiv}, author = {Elkind, Edith and Goldberg, Leslie A. and Goldberg, Paul W.}, citeulike-article-id = {1001111}, citeulike-linkout-0 = {http://arxiv.org/abs/cs.GT/0606044}, citeulike-linkout-1 = {http://arxiv.org/pdf/cs.GT/0606044}, day = {26}, eprint = {cs.GT/0606044}, keywords = {frugal, truthful, vertexcover}, month = {Jul}, posted-at = {2006-12-19 00:14:43}, priority = {0}, title = {Frugality ratios and improved truthful mechanisms for vertex cover}, url = {http://arxiv.org/abs/cs.GT/0606044}, year = {2006} }

TY - ELEC ID - citeulike:1001111 L3 - citeulike-article-id:1001111 N2 - In {\em set-system auctions}, there is a task than can be completed by several overlapping teams of selfish agents, and the centre's goal is to hire one of these teams 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 {\em 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. We bound its frugality ratio. We show that both the solution quality and the frugality ratio of our auction are within a constant factor of optimal; this is the first auction for this problem to have these properties. Moreover, we show how to transform any truthful auction into a frugal one while preserving the approximation ratio. Also, we consider two natural modifications of the definition of Karlin et al., and we analyse the properties of the resulting payment bounds, such as monotonicity, computational hardness, and robustness with respect to the draw-resolution rule. We study the relationships between the different payment bounds, both for general set systems and for specific set-system auctions, such as path auctions and vertex-cover auctions. We use these new definitions in the proof of our main result for vertex-cover auctions via a bootstrapping technique, which may be of independent interest. TI - Frugality ratios and improved truthful mechanisms for vertex cover KW - frugal KW - truthful KW - vertexcover AU - Elkind, Edith AU - Goldberg, Leslie AU - Goldberg, Paul PY - 2006/Jul/26/ UR - http://arxiv.org/abs/cs.GT/0606044 ER -