optl

1 files changed, 2 insertions, 2 deletions

diff --git a/main.tex b/main.tex
index 269bc7a..4fa6e74 100644
--- a/main.tex
+++ b/main.tex
@@ -282,7 +282,7 @@ following lemma, which establishes that $OPT'$, the optimal value \eqref{relax}
         + 2\max_{i\in\mathcal{N}}V(i)$
     %\end{displaymath}
 \end{lemma}
-Note that the lower bound $OPT(L, B) \geq  OPT
+Note that the lower bound $OPT' \geq  OPT
 $ also holds trivially, as $L$ is a fractional relaxation of $V$ over $\mathcal{N}$.
 The proof of Lemma~\ref{lemma:relaxation} is our main technical contribution, and can be found in Section \ref{sec:relaxation}.
 Using this lemma, we can complete the proof of Theorem~\ref{thm:main} by showing that, %\begin{lemma}\label{lemma:approx}
@@ -605,7 +605,7 @@ Having bound the ratio between the partial derivatives, we now bound the ratio $
     function $V$. Hence, the ratio is equal to 1 on the vertices.
 \end{proof}
  To prove Lemma~\ref{lemma:relaxation},   let us consider a feasible point $\lambda^*\in[0,1]^{n}$ such that $L(\lambda^*)
-    = OPT(L, B)$. By applying Lemma~\ref{lemma:relaxation-ratio}
+    = OPT'$. By applying Lemma~\ref{lemma:relaxation-ratio}
     and Lemma~\ref{lemma:rounding} we get a feasible point $\bar{\lambda}$ with at most
     one fractional component such that:
     \begin{equation}\label{eq:e1}