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authorStratis Ioannidis <stratis@Stratiss-MacBook-Air.local>2013-09-22 07:55:14 +0200
committerStratis Ioannidis <stratis@Stratiss-MacBook-Air.local>2013-09-22 07:55:14 +0200
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downloadrecommendation-cc1eea524d8fd1314d85fe7b56cddd95fd75302d.tar.gz
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@@ -42,7 +42,7 @@ We present a polynomial time mechanism scheme for \SEDP{} that is approximately
In contrast to this, we show that no truthful, budget-feasible mechanisms are possible for \SEDP{} within a factor 2 approximation.
\smallskip
-We note that the objective \eqref{obj} is submodular. Using this fact, applying previous results on budget feasible mechanism design under general submodular objectives~\cite{singer-mechanisms,chen} would yield either a deterministic, truthful, constant-approximation mechanism that requires exponential time, or a non-deterministic, (universally) truthful, poly-time mechanism that yields a constant approximation ratio only \emph{in expectation} (\emph{i.e.}, its approximation guarantee for a given instance may in fact be unbounded).
+We note that the objective \eqref{obj} is submodular. Using this fact, applying previous results on budget feasible mechanism design under general submodular objectives~\cite{singer-mechanisms,chen} would yield either a deterministic, truthful, constant-approximation mechanism that requires exponential time, or a non-determi\-nis\-tic, (universally) truthful, poly-time mechanism that yields a constant approximation ratio only \emph{in expectation} (\emph{i.e.}, its approximation guarantee for a given instance may in fact be unbounded).
\end{itemize}