From c5c7e55c0d14009d47d838efad3a799cb59a3d77 Mon Sep 17 00:00:00 2001
From: Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>
Date: Sun, 7 Jul 2013 00:29:53 -0700
Subject: app:properties

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

(limited to 'main.tex')

diff --git a/main.tex b/main.tex
index 0dfa162..324f11f 100644
--- a/main.tex
+++ b/main.tex
@@ -57,7 +57,7 @@ To obtain this result, we use the following modified version of Myerson's theore
 %variant of Myerson's theorem.
 
 \begin{lemma}\label{thm:myerson-variant}
-\sloppy A normalized mechanism $\mathcal{M} = (S,p)$ for a single parameter auction is
+ A normalized mechanism $\mathcal{M} = (S,p)$ for a single parameter auction is
 $\delta$-truthful if:
 (a) $S$ is $\delta$-monotone, \emph{i.e.}, for any agent $i$ and $c_i' \leq
 c_i-\delta$, for any
@@ -65,11 +65,8 @@ fixed costs $c_{-i}$ of agents in $\mathcal{N}\setminus\{i\}$, $i\in S(c_i,
 c_{-i})$ implies $i\in S(c_i', c_{-i})$, and (b)
  agents are paid \emph{threshold payments}, \emph{i.e.}, for all $i\in S(c)$, $p_i(c)=\inf\{c_i': i\in S(c_i', c_{-i})\}$.
 \end{lemma}
-\fussy
-
-We can now state our main result, which is proved in Appendix~\ref{sec:proofofmainthm}:
+Lemma~\ref{thm:myerson-variant} allow us to incorporate our relaxation in the above framework, yielding the following theorem:
 \begin{theorem}\label{thm:main}
-    \sloppy
     For any $\delta>0$, and any $\epsilon>0$,  there exists a $\delta$-truthful, individually rational
     and budget feasible mechanim for \EDP{} that runs in time
     $O\big(poly(n, d, \log\log\frac{B}{b\varepsilon\delta})\big)$
@@ -82,6 +79,7 @@ We can now state our main result, which is proved in Appendix~\ref{sec:proofofma
          \simeq 12.98V(S^*) + \varepsilon.$
 %    \end{align*}
 \end{theorem}
+The proof of the theorem, as well as our proposed mechanism, can be found in Appendix~\ref{sec:proofofmainthm}.
 In addition, we prove the following simple lower bound, proved in Appendix~\ref{proofoflowerbound}.
 
 \begin{theorem}\label{thm:lowerbound}
@@ -89,3 +87,5 @@ There is no $2$-approximate, truthful, budget feasible, individually rational
 mechanism for EDP. 
 \end{theorem}
 
+
+
-- 
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