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Antti H S Laaksonen 2017-02-21 01:17:36 +02:00
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luku20.tex
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@ -89,7 +89,7 @@ It is easy see that this flow is maximum,
because the total capacity of the edges
leading to the sink is $7$.
\subsubsection{Minimum cuts}
\subsubsection{Minimum cut}
\index{cut}
\index{minimum cut}
@ -157,7 +157,7 @@ The algorithm also helps us to understand
\index{Ford–Fulkerson algorithm}
The \key{Ford–Fulkerson algorithm} finds
The \key{Ford–Fulkerson algorithm} \cite{for56} finds
the maximum flow in a graph.
The algorithm begins with an empty flow,
and at each step finds a path in the graph
@ -430,7 +430,7 @@ by using one of the following techniques:
\index{Edmonds–Karp algorithm}
The \key{Edmonds–Karp algorithm}
The \key{Edmonds–Karp algorithm} \cite{edm72}
is a variant of the
Ford–Fulkerson algorithm that
chooses each path so that the number of edges
@ -459,7 +459,7 @@ because depth-first search can be used for finding paths.
Both algorithms are efficient enough for problems
that typically appear in programming contests.
\subsubsection{Minimum cut}
\subsubsection{Minimum cuts}
\index{minimum cut}
@ -779,7 +779,7 @@ such that each pair is connected with an edge and
each node belongs to at most one pair.
There are polynomial algorithms for finding
maximum matchings in general graphs,
maximum matchings in general graphs \cite{edm65},
but such algorithms are complex and do
not appear in programming contests.
However, in bipartite graphs,