From 385334421230a9a4f7422817cc2fae224fd561da Mon Sep 17 00:00:00 2001
From: Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>
Date: Thu, 4 Jul 2013 18:53:24 -0700
Subject: wording, proof, algo

---
 appendix.tex | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

(limited to 'appendix.tex')

diff --git a/appendix.tex b/appendix.tex
index 682fce2..bf163b4 100644
--- a/appendix.tex
+++ b/appendix.tex
@@ -476,12 +476,12 @@ Using Lemma~\ref{lemma:barrier} concludes the proof of the running time.\qed
 
 \section{Proof of Theorem~\ref{thm:main}}\label{sec:proofofmainthm}
 
-We now present the proof of Theorem~\ref{thm:main}. $\delta$-truthfulness and
-individual rationality follow from $\delta$-monotonicity and threshold
-payments. $\delta$-monotonicity and budget feasibility follow the same steps as the
-analysis of \citeN{chen}; for the sake of completeness, we restate their proof
-here.
+We now present the proof of Theorem~\ref{thm:main}. We use the notation $OPT_{-i^*}$ to denote the optimal value of \EDP{} when the maximum value element $i^*$ is  excluded. We also use $OPT'_{-i^*}$ the approximation computed by the $\delta$-decreasing, $\epsilon$-accurate approximation of $L^*_{c_{-i^*}}$, as defined in Algorithm~\ref{mechanism}.
 
+The properties of $\delta$-truthfulness and
+individual rationality follow from $\delta$-monotonicity and threshold
+payments. $\delta$-monotonicity and budget feasibility follow  similar steps as the
+analysis of \citeN{chen}, adapted to account for $\delta$-monotonicity:
 \begin{lemma}\label{lemma:monotone}
 Our mechanism for \EDP{} is $\delta$-monotone and budget feasible.
 \end{lemma}
-- 
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