From cec9b298f548ce44fe5eaecf71c04d65c95de993 Mon Sep 17 00:00:00 2001
From: Stratis Ioannidis <stratis@stratis-Latitude-E6320.(none)>
Date: Sun, 4 Nov 2012 23:38:08 -0800
Subject: opts

---
 problem.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'problem.tex')

diff --git a/problem.tex b/problem.tex
index 2a40185..98ca4ac 100644
--- a/problem.tex
+++ b/problem.tex
@@ -49,7 +49,7 @@ knowledge; the objective of the buyer in this context is to select a set $S$
 maximizing the value $V(S)$ subject to the constraint $\sum_{i\in S} c_i\leq
 B$. We write:
 \begin{equation}\label{eq:non-strategic}
-    OPT(V,\mathcal{N}, B) = \max_{S\subseteq\mathcal{N}} \left\{V(S) \mid
+    OPT = \max_{S\subseteq\mathcal{N}} \left\{V(S) \mid
     \sum_{i\in S}c_i\leq B\right\}
 \end{equation}
 for the optimal value achievable in the full-information case. %\stratis{Should be $OPT(V,c,B)$\ldots better drop the arguments here and introduce them wherever necessary.}
@@ -82,7 +82,7 @@ A mechanism is truthful iff  every $i \in \mathcal{N}$ and every two cost vector
     \eqref{eq:non-strategic}. Formally, there must exist some $\alpha\geq 1$
     such that:
     \begin{displaymath}
-        OPT(V,\mathcal{N}, B) \leq \alpha V(S).
+        OPT \leq \alpha V(S).
     \end{displaymath}
     The approximation ratio captures the \emph{price of truthfulness}, \emph{i.e.},  the relative value loss incurred by adding the truthfulness constraint. % to the value function maximization.
     \item \emph{Computational efficiency.} The allocation and payment function
-- 
cgit v1.2.3-70-g09d2

