From: Martin Mares Date: Sat, 19 Apr 2008 15:24:01 +0000 (+0200) Subject: Bits of introduction. X-Git-Tag: printed~77 X-Git-Url: http://mj.ucw.cz/gitweb/?a=commitdiff_plain;h=77268df187a9df3c4e1e2fe1950adb288c67bbe1;p=saga.git Bits of introduction. --- diff --git a/mst.tex b/mst.tex index 2cfe5d0..06a1af8 100644 --- 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. %--------------------------------------------------------------------------------