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References etc.

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Antti H S Laaksonen 2017-02-25 17:57:10 +02:00
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3
chapter10.tex
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@ -391,7 +391,8 @@ to change an iteration over permutations into
an iteration over subsets, so that an iteration over subsets, so that
the dynamic programming state the dynamic programming state
contains a subset of a set and possibly contains a subset of a set and possibly
some additional information. some additional information\footnote{This technique was introduced in 1962
by M. Held and R. M. Karp \cite{hel62}.}.
The benefit in this is that The benefit in this is that
$n!$, the number of permutations of an $n$ element set, $n!$, the number of permutations of an $n$ element set,

14
chapter15.tex
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@ -123,7 +123,8 @@ maximum spanning trees by processing the edges in reverse order.
\index{Kruskal's algorithm} \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 only contains the nodes of the graph
and does not contain any edges. and does not contain any edges.
Then the algorithm goes through the 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: Two $O(\log n)$ time operations are supported:
the \texttt{union} operation joins two sets, the \texttt{union} operation joins two sets,
and the \texttt{find} operation finds the representative 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} \subsubsection{Structure}
@ -567,7 +572,10 @@ the smaller set to the larger set.
\index{Prim's algorithm} \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. for finding a minimum spanning tree.
The algorithm first adds an arbitrary node The algorithm first adds an arbitrary node
to the tree. to the tree.

15
list.tex
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@ -107,6 +107,16 @@
Computer Science and Computational Biology}, Computer Science and Computational Biology},
Cambridge University Press, 1997. Cambridge University Press, 1997.
\bibitem{hel62}
M. Held and R. M. Karp.
A dynamic programming approach to sequencing problems.
\emph{Journal of the Society for Industrial and Applied Mathematics}, 10(1):196--210, 1962.
\bibitem{hop71}
J. E. Hopcroft and J. D. Ullman.
A linear list merging algorithm.
Technical report, Cornell University, 1971.
\bibitem{hor74} \bibitem{hor74}
E. Horowitz and S. Sahni. E. Horowitz and S. Sahni.
Computing partitions with applications to the knapsack problem. Computing partitions with applications to the knapsack problem.
@ -179,6 +189,11 @@
Gaussian elimination is not optimal. Gaussian elimination is not optimal.
\emph{Numerische Mathematik}, 13(4):354--356, 1969. \emph{Numerische Mathematik}, 13(4):354--356, 1969.
\bibitem{tar75}
R. E. Tarjan.
Efficiency of a good but not linear set union algorithm.
\emph{Journal of the ACM}, 22(2):215--225, 1975.
\bibitem{tar84} \bibitem{tar84}
R. E. Tarjan and U. Vishkin. R. E. Tarjan and U. Vishkin.
Finding biconnected componemts and computing tree functions in logarithmic parallel time. Finding biconnected componemts and computing tree functions in logarithmic parallel time.