Bits of introduction.

diff --git a/mst.tex b/mst.tex
index 2cfe5d0f7820bd5642ac9cf4879a35c32e90a6a1..06a1af8648a1dfa73d056fda3f53f8887b5eace5 100644 (file)
--- a/mst.tex
+++ b/mst.tex
@@ -41,15 +41,16 @@ spanning tree problem was one of the central topics of the flourishing new
 disciplines, the previous work was not well known and the algorithms had to be
 rediscovered several times.
 
-Recently, several significantly faster algorithms were discovered, most notably the
-$\O(m\timesbeta(m,n))$-time algorithm by Fredman and Tarjan \cite{ft:fibonacci} and
-algorithms with inverse-Ackermann type complexity by Chazelle \cite{chazelle:ackermann}
-and Pettie \cite{pettie:ackermann}.
-
-\FIXME{Write the rest of the history.}
-
-This chapter attempts to survey the important algorithms for finding the MST and it
-also presents several new ones.
+In the next 50 years, several significantly faster algorithms were discovered, ranging
+from the $\O(m\timesbeta(m,n))$ time algorithm by Fredman and Tarjan \cite{ft:fibonacci},
+over algorithms with inverse-Ackermann type complexity by Chazelle \cite{chazelle:ackermann}
+and Pettie \cite{pettie:ackermann}, to another algorithm by Pettie \cite{pettie:optimal}
+whose time complexity is provably optimal.
+
+In the upcoming chapters, we will explore this colorful universe of MST algorithms.
+We will meet the standard works of the classics, the clever ideas of their successors,
+various approaches to the problem including randomization and solving of important
+special cases.
 
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