From c7ca7fb461ec2044f8aefcedfcd903d8b5945fc1 Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Sun, 22 Sep 2013 18:28:41 -0400
Subject: Last fixes

---
 appendix.tex      | 2 +-
 approximation.tex | 4 ++--
 main.tex          | 2 +-
 notes.bib         | 4 +---
 paper.tex         | 2 --
 5 files changed, 5 insertions(+), 9 deletions(-)

diff --git a/appendix.tex b/appendix.tex
index 1a5bcc5..6926e00 100755
--- a/appendix.tex
+++ b/appendix.tex
@@ -880,7 +880,7 @@ Placing the expression of $C$ in \eqref{eq:bound1} and \eqref{eq:bound2}
 gives the approximation ratio in \eqref{approxbound}, and concludes the proof
 of Theorem~\ref{thm:main}.\hspace*{\stretch{1}}\qed
 
-Finally, we prove the lower bound stated in Theorem~\ref{thm:main}
+Finally, we prove the lower bound stated in Theorem~\ref{thm:main}.
 Suppose, for contradiction, that such a mechanism exists. From Myerson's Theorem \cite{myerson}, a single parameter auction is truthful if and only if the allocation function is monotone and agents are paid theshold payments. Consider two
 experiments with dimension $d=2$, such that $x_1 = e_1=[1 ,0]$, $x_2=e_2=[0,1]$
 and $c_1=c_2=B/2+\epsilon$. Then, one of the two experiments, say, $x_1$, must
diff --git a/approximation.tex b/approximation.tex
index 901e1dd..dc39e5b 100755
--- a/approximation.tex
+++ b/approximation.tex
@@ -127,8 +127,8 @@ In other words, $f$ is $\delta$-decreasing if increasing any coordinate by $\del
 
 \begin{proposition}\label{prop:monotonicity}
     For any $\delta\in(0,1]$ and any $\varepsilon\in(0,1]$,
-    there exists an algorithm computes a $\delta$-decreasing,
+    there exists an algorithm which computes a $\delta$-decreasing,
     $\varepsilon$-accurate approximation of $L^*_c$. The running time of the
     algorithm is $O\big(poly(n, d, \log\log\frac{B}{b\varepsilon\delta})\big)$.
 \end{proposition}
-The proof and the  algorithm (Algorithm~\ref{alg:monotone}) are in Appendix~\ref{proofofproprelaxation}.
+The proof and the  algorithm (Algorithm~\ref{alg:monotone}) are in Appendix~\ref{proofofpropmonotonicity}.
diff --git a/main.tex b/main.tex
index a01d780..66ef875 100755
--- a/main.tex
+++ b/main.tex
@@ -20,7 +20,7 @@ The $\delta$-decreasing, $\epsilon$-accurate algorithm solving the convex optimi
 Furthemore, there is no $2$-approximate, truthful, budget feasible, individually rational
 mechanism for EDP. 
 \end{theorem}
-The detailed description of our proposed mechanism (see Algorithm~\ref{mechanism}), as well as the proof of the theorem can be found in Appendix~\ref{sec:proofofmainthm}.
+The detailed description of our proposed mechanism (Algorithm~\ref{mechanism}), as well as the proof of the theorem can be found in Appendix~\ref{sec:proofofmainthm}.
 
 
 
diff --git a/notes.bib b/notes.bib
index 8a26399..0cd0372 100755
--- a/notes.bib
+++ b/notes.bib
@@ -104,10 +104,8 @@ year = 2012
 @incollection{calinescu2007maximizing,
   title={Maximizing a submodular set function subject to a matroid constraint},
   author={Calinescu, Gruia and Chekuri, Chandra and P{\'a}l, Martin and Vondr{\'a}k, Jan},
-  booktitle={Integer programming and combinatorial optimization},
-  pages={182--196},
+  booktitle={IPCO},
   year={2007},
-  publisher={Springer}
 }
 
 
diff --git a/paper.tex b/paper.tex
index 242146b..c741aaa 100755
--- a/paper.tex
+++ b/paper.tex
@@ -38,10 +38,8 @@
 \input{main}
 \section{Conclusions}\label{sec:concl}
 \input{conclusion}
-\begin{comment}
 \section*{Acknowledgments}
 \input{ack}
-\end{comment}
 \bibliographystyle{splncsnat}
 \begin{footnotesize}
 \bibliography{notes}
-- 
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