Abstract
In a STACS 2003 paper, Talwar analyses the overpayment the VCG mechanism incurs for ensuring truthfulness in auction. Among other results, he studies k-Set Cover (given a universe U and a collection of sets S 1, S 2, ..., S q , each having a cost c(S i ) and at most k elements of U, find a minimum cost subcollection, called cover, whose union equals U) and shows that the payment of the optimum cover OPT is at most kc(OPT′), where OPT′ is the best cover disjoint from the optimum cover. For k ≥ 3, k-Set Cover is known to be NP-Hard, and thus truthful mechanisms based on approximation algorithms are desirable. We show that the payment incurred by two approximation algorithms (including the Greedy algorithm) is bounded by (k – 1) c(OPT) + kc(OPT′). The same approximation algorithms have payment bounded by k (c(OPT) + c(OPT′) ) when applied to more general set systems, which include k-Polymatroid Cover, a problem with applications in Steiner Tree computations. If q is such that an element in a k-Set-Cover instance appears in at most q sets, we show that the payment of our algorithms is bounded by qk 2 times the payment of the optimum algorithm.
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Calinescu, G. (2004). Bounding the Payment of Approximate Truthful Mechanisms. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_21
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DOI: https://doi.org/10.1007/978-3-540-30551-4_21
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