References etc.

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Antti H S Laaksonen 2017-02-25 17:57:10 +02:00
parent e0c4736a7c
commit ef1e3abfd1
3 changed files with 28 additions and 4 deletions

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@ -123,7 +123,8 @@ maximum spanning trees by processing the edges in reverse order.
\index{Kruskal's algorithm}
In \key{Kruskal's algorithm} \cite{kru56}, the initial spanning tree
In \key{Kruskal's algorithm}\footnote{The algorithm was published in 1956
by J. B. Kruskal \cite{kru56}.}, the initial spanning tree
only contains the nodes of the graph
and does not contain any edges.
Then the algorithm goes through the edges
@ -409,7 +410,11 @@ belongs to more than one set.
Two $O(\log n)$ time operations are supported:
the \texttt{union} operation joins two sets,
and the \texttt{find} operation finds the representative
of the set that contains a given element.
of the set that contains a given element\footnote{The structure presented here
was introduced in 1971 by J. D. Hopcroft and J. D. Ullman \cite{hop71}.
Later, in 1975, R. E. Tarjan studied a more sophisticated variant
of the structure \cite{tar75} that is discussed in many algorithm
textbooks nowadays.}.
\subsubsection{Structure}
@ -567,7 +572,10 @@ the smaller set to the larger set.
\index{Prim's algorithm}
\key{Prim's algorithm} \cite{pri57} is an alternative method
\key{Prim's algorithm}\footnote{The algorithm is
named after R. C. Prim who published it in 1957 \cite{pri57}.
However, the same algorithm was discovered already in 1930
by V. Jarník.} is an alternative method
for finding a minimum spanning tree.
The algorithm first adds an arbitrary node
to the tree.