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Applied edits to network flow handout

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2023-01-08 09:10:54 -08:00
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Advanced/Graph Algorithms/parts/02 residual.tex
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\section{Residual Graphs}
As our network gets bigger, finding a maximum flow by hand becomes much more difficult. It will be convenient to have an algorithm that finds a maximal flow in any network.
It is hard to find a maximum flow for a large network by hand. \\
We need to create an algorithm to accomplish this task.
\vspace{1ex}
The first thing we'll need to construct such an algorithm is a \textit{residual graph}.
The first thing we'll is the notion of a \textit{residual graph}.
\vspace{2ex}
\hrule
@ -202,11 +203,9 @@ If it isn't, find a maximal flow. \\
\problem{}
Show that...
\begin{enumerate}
\item A maximal flow exists in every network with integral\footnotemark{} edge weights.
\item A maximal flow exists in every network with integral edge weights.
\item Every edge in this flow carries an integral amount of flow
\end{enumerate}
\footnotetext{Integral = \say{integer} as an adjective.}
\vfill
\pagebreak