From 7ff4a4d46dbd64cd8bc7c07d0c7f11f13779443c Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Mon, 10 Jun 2013 19:09:15 +0200
Subject: Moving our two main results to a section preceding the introduction
 of our mechanism

---
 appendix.tex | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

(limited to 'appendix.tex')

diff --git a/appendix.tex b/appendix.tex
index b1d35d6..53bc328 100644
--- a/appendix.tex
+++ b/appendix.tex
@@ -22,7 +22,8 @@ Our mechanism for \EDP{} is monotone and budget feasible.
         \frac{B}{2}\frac{V(S_i\cup\{i\})-V(S_i)}{V(S_i\cup\{i\})}
          \leq \frac{B}{2}\frac{V(S_i'\cup\{i\})-V(S_i')}{V(S_i'\cup\{i\})}
     \end{align*}
-    by the monotonicity and submodularity  of $V$. Hence  $i\in S_G'$. As $OPT'_{-i^*}$,  is the optimal value of \eqref{relax} under relaxation $L$ when $i^*$ is excluded from $\mathcal{N}$, reducing the costs can only increase this value, so under $c'_i\leq c_i$ the greedy set is still allocated and $s_i(c_i',c_{-i}) =1$.
+    by the monotonicity and submodularity  of $V$. Hence  $i\in S_G'$. As
+    $OPT'_{-i^*}$,  is the optimal value of \eqref{eq:primal} under relaxation $L$ when $i^*$ is excluded from $\mathcal{N}$, reducing the costs can only increase this value, so under $c'_i\leq c_i$ the greedy set is still allocated and $s_i(c_i',c_{-i}) =1$.
     Suppose now that when $i$ reports $c_i$, $OPT'_{-i^*} < C V(i^*)$. Then $s_i(c_i,c_{-i})=1$ iff $i = i^*$. 
     Reporting $c_{i^*}'\leq c_{i^*}$ does not change $V(i^*)$ nor
     $OPT'_{-i^*} \leq C V(i^*)$; thus $s_{i^*}(c_{i^*}',c_{-i^*})=1$, so the mechanism is monotone.
-- 
cgit v1.2.3-70-g09d2

