From cd7c3fe857f1ec8972959be2a5a9b73c6f4167ef Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Mon, 11 Feb 2013 01:06:19 -0800
Subject: Small fixes to section 3 and 4

---
 main.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'main.tex')

diff --git a/main.tex b/main.tex
index 1a1d016..f11c4ee 100644
--- a/main.tex
+++ b/main.tex
@@ -26,7 +26,7 @@ OPT \leq \frac{e}{e-1}\big( 3 V(S_G) + 2 V(i^*)\big).
 \end{displaymath}
 \end{lemma}
 This lemma immediately implies that the following algorithm:
-\begin{equation}\label{eq:algorithm}
+\begin{equation}\label{eq:max-algorithm}
 \textbf{if}\; V(\{i^*\}) \geq V(S_G)\; \textbf{return}\; \{i^*\}
 \;\textbf{else return}\; S_G
 \end{equation}
@@ -34,7 +34,7 @@ has an approximation ratio of $\frac{5e}{e-1}$.
 
 \subsection*{Submodular maximization in the strategic case}
 
-In the strategic case, Algorithm~\ref{eq:algorithm} breaks incentive
+In the strategic case, Algorithm~\eqref{eq:max-algorithm} breaks incentive
 compatibility. Indeed, \citeN{singer-influence} notes that this allocation
 function is not monotone, which implies by Myerson's theorem
 (Theorem~\ref{thm:myerson}) that the resulting mechanism is not truthful.
@@ -47,7 +47,7 @@ full-information case after removing $i^*$ from the set $\mathcal{N}$:
 \end{equation}
 \citeN{singer-mechanisms} and \citeN{chen} prove that using the following
 allocation:
-\begin{displaymath}\label{eq:algorithm}
+\begin{displaymath}
 \textbf{if}\; V(\{i^*\}) \geq C. OPT_{-i^*}\; \textbf{return}\; \{i^*\}
 \;\textbf{else return}\; S_G
 \end{displaymath}
-- 
cgit v1.2.3-70-g09d2

