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Diffstat (limited to 'approximation.tex')
| -rw-r--r-- | approximation.tex | 2 |
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diff --git a/approximation.tex b/approximation.tex index 670352b..7c3c47d 100644 --- a/approximation.tex +++ b/approximation.tex @@ -1,4 +1,4 @@ -Previous approaches towards designing truthful, budget feasible mechanisms for \textsc{Knapsack}~\cite{chen} and the \textsc{Coverage}~\cite{singer-influence} build upon polynomial-time algorithms that compute an approximation of $OPT$, the optimal value in the full information case. Crucially, to be used in designing a truthful mechanism, such algorithms need also to be \emph{monotone}, in the sense that decreasing any of the costs $c_i$ leads to an increase of the estimate of $OPT$. Both in the cases of \textsc{Knapsack}~\cite{chen} and~\textsc{Coverage}, as well as in the case of \EDP{}, the monotonicity requirement prevents using traditional approximation algorithms for approximating any of the above problems. +Previous approaches towards designing truthful, budget feasible mechanisms for \textsc{Knapsack}~\cite{chen} and \textsc{Coverage}~\cite{singer-influence} build upon polynomial-time algorithms that compute an approximation of $OPT$, the optimal value in the full information case. Crucially, to be used in designing a truthful mechanism, such algorithms need also to be \emph{monotone}, in the sense that decreasing any of the costs $c_i$ leads to an increase of the estimate of $OPT$. In the cases of \textsc{Knapsack} and~\textsc{Coverage}, as well as in the case of \EDP{}, monotonicity prevents using traditional approximation algorithms. We address this issue by designing a convex relaxation of \EDP{}, and showing that it well approximates $OPT$. |