From ef1e3abfd1ed941b2337b55044e660785573bbca Mon Sep 17 00:00:00 2001
From: Antti H S Laaksonen <ahslaaks@cs.helsinki.fi>
Date: Sat, 25 Feb 2017 17:57:10 +0200
Subject: [PATCH] References etc.

---
 chapter10.tex |  3 ++-
 chapter15.tex | 14 +++++++++++---
 list.tex      | 15 +++++++++++++++
 3 files changed, 28 insertions(+), 4 deletions(-)

diff --git a/chapter10.tex b/chapter10.tex
index 13cce68..273e7c7 100644
--- a/chapter10.tex
+++ b/chapter10.tex
@@ -391,7 +391,8 @@ to change an iteration over permutations into
 an iteration over subsets, so that
 the dynamic programming state
 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
 $n!$, the number of permutations of an $n$ element set,
diff --git a/chapter15.tex b/chapter15.tex
index 4f7df84..4be2643 100644
--- a/chapter15.tex
+++ b/chapter15.tex
@@ -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.
diff --git a/list.tex b/list.tex
index 70242eb..4bee692 100644
--- a/list.tex
+++ b/list.tex
@@ -107,6 +107,16 @@
   Computer Science and Computational Biology},
   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}
   E. Horowitz and S. Sahni.
   Computing partitions with applications to the knapsack problem.
@@ -179,6 +189,11 @@
   Gaussian elimination is not optimal.
   \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}
   R. E. Tarjan and U. Vishkin.
   Finding biconnected componemts and computing tree functions in logarithmic parallel time.