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main.tex

@@ -146,6 +146,9 @@ Note that Thorup used a greedy way to construct the cocycle $C$. Elements in $C$
 These facts implies that the minimum $k$-cocycle has a smaller value $\sum c(e)u^*(e)$ than $C$.
 
 However, Lemma~7 in \cite{Thorup_2008} does not generalize to all matroids and we need to take a close look at the construction of $C$.
+Let $k'$ be $r(E)-r(F^*)$ and we want to find the minimum $k$-cocycle.
+Basically we need to do random contraction on $M/ F^*$. Let $\mathcal X$ be the set $\set{X|X=B\setminus F^* \land r(X)=k'}$. That is, we consider all bases that hitten by the $k'$-cocycle exactly $k'$ times and for each of them we collect the intersection with the $k'$-cocycle.
+...
 
 \subsection{Support size}