From 560eb3da4a23ed3317f8678688f2a55fc7d3c1bf Mon Sep 17 00:00:00 2001
From: Stratis Ioannidis <stratis@Stratiss-MacBook-Air.local>
Date: Sun, 22 Sep 2013 23:22:03 +0200
Subject: done

---
 approximation.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'approximation.tex')

diff --git a/approximation.tex b/approximation.tex
index 546961f..901e1dd 100755
--- a/approximation.tex
+++ b/approximation.tex
@@ -34,7 +34,7 @@ In the first part of this section, we address this issue by designing a convex r
 A classical way of relaxing combinatorial optimization problems is 
 \emph{relaxing by expectation}, using the so-called \emph{multi-linear}
 extension of the objective function $V$ (see, \emph{e.g.}, \cite{calinescu2007maximizing,vondrak2008optimal,dughmi2011convex}).
-This is because this extension can yield approximation guarantees for a wide class of combinatorial problems through \emph{pipage rounding}, a technique proposed by \citeN{pipage}. Crucially for our purposes, such relaxations in general preserve monotonicity which, as discussed, is required in mechanism design.
+This is because this extension can yield approximation guarantees for a wide class of combinatorial problems through \emph{pipage rounding}, a technique proposed by \citeN{pipage}.  In general, such relaxations preserve monotonicity which, as discussed, is required in mechanism design.
 
 Formally, let $P_\mathcal{N}^\lambda$ be a probability distribution over $\mathcal{N}$ parametrized by $\lambda\in [0,1]^n$, where a set $S\subseteq \mathcal{N}$ sampled from  $P_\mathcal{N}^\lambda$ is constructed as follows:  each $i\in \mathcal{N}$ is selected to be in $S$ independently with probability $\lambda_i$, \emph{i.e.},
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