Corrections of the Preface.

diff --git a/pref.tex b/pref.tex
index 3bbbf26b7eea9b02cb92bb88565dced160cde6c7..dfb726e3b06ca1fa5791ebe5d784cee1be5aef5c 100644 (file)
--- a/pref.tex
+++ b/pref.tex
@@ -15,19 +15,19 @@ with the intricate details of various models of computation and even of arithmet
 itself.
 
 I have tried to cover all known important results on both problems and unite them
-in a~single coherent theory. At many places, I have tried to contribute my own
+in a~single coherent theory. At many places, I have attempted to contribute my own
 little stones to this mosaic: several new results, simplifications of existing
 ones, and last, but not least filling in important details where the original
 authors have missed some.
 
 When compared with the earlier surveys on the minimum spanning trees, most
 notably Graham and Hell \cite{gh:history} and Eisner \cite{eisner:tutorial},
-this work includes many of the recent advances, the dynamic algorithms and
+this work adds many of the recent advances, the dynamic algorithms and
 also the relationship with computational models. No previous work covering
-the ranking problems in entirety is known.
+the ranking problems in their entirety is known.
 
-The early parts of this thesis also served as a~basis for the course on graph
-algorithms which I was teaching at our faculty during 2006 and~2007. They are
+The early parts of this thesis also served as a~basis for a~course on graph
+algorithms which I was teaching at our faculty during years 2006 and~2007. They are
 included in the textbook \cite{mm:ga} which I have written for this course.
 
 \def\ss#1{\medskip\>{\bo #1}\enspace\eatspaces}
@@ -43,17 +43,17 @@ included in the textbook \cite{mm:ga} which I have written for this course.
   in the original paper. Not published yet.
 \:The ranking algorithms in Sections \ref{ranksect} to \ref{kpranksect} are results of joint research with Milan Straka.
   Published in \cite{mm:rank}.
-\:The remaining sections of Chapter \ref{rankchap} contain unpublished original research.
+\:The remaining sections of Chapter \ref{rankchap} contain unpublished original results.
 \endlist
 
 \ss{Other minor contributions}
 
 \itemize\ibull
-\:The flattening procedure in Section \ref{bucketsort}. Published in \cite{mm:mst}.
+\:The flattening procedure in Section \ref{bucketsort}. Included in \cite{mm:mst}.
 \:The unified view of vector computations in Section \ref{bitsect}. Published
-  in the textbook \cite{mm:ga}. The main ideas of this section were also published
+  in the textbook \cite{mm:ga}. The main ideas of this section were also included
   in the yearbook of the Czech Mathematical Olympiad \cite{horak:mofivefour}.
-\:Several simplifications of the soft heaps in Section \ref{shsect}.
+\:Slight simplifications of the soft heaps and their analysis in Section \ref{shsect}.
 \:The dynamic MST algorithm for graphs with limited edge weights in Section \ref{dynmstsect}.
 \endlist
 
@@ -64,15 +64,17 @@ included in the textbook \cite{mm:ga} which I have written for this course.
 First of all, I~would like to thank my supervisor, Jaroslav Ne\v{s}et\v{r}il, for
 introducing me to the world of discrete mathematics and gently guiding my attempts
 to explore it with his deep insight. I~am very grateful to all members of the
-Department of Applied Mathematics and of the Institute for Theoretical Computer
-Science for the work environment which was both friendly and highly inspiring.
+Department of Applied Mathematics and the Institute for Theoretical Computer
+Science for the work environment which was friendly and highly inspiring.
+I~cannot forget the participants of the department's seminars,
+who have listened to my talks and provided lots of important feedback.
 I~also send my acknowledgements to the members of the Math department at ETH Z\"urich and of DIMACS
 at the Rutgers University (especially to J\'anos Koml\'os) where I~spent several
 pleasant months working on what finally become a~part of this thesis.
 
 I~also thank to my family for supporting me during the plentiful years of my study,
 to my girlfriend Ani\v{c}ka for lots of patience when I~was caught up by my work and
-hardly speaking, to all the polar bears of Kobylisy for their furry presence, and
+hardly speaking at all, to all the polar bears of Kobylisy for their furry presence, and
 finally to our cats Minuta and Dami\'an for their mastership in hiding my
 papers, which has frequently forced me to think of new ways of looking at problems
 when the old ones were impossible to find.
@@ -89,7 +91,7 @@ consistently in the common literature.
 To avoid piling up too many symbols at places that speak about a~single fixed graph,
 this graph is always called~$G$, its set of vertices and edges are denoted by $V$
 and~$E$ respectively, and I~also use~$n$ for the number of its vertices and $m$~for
-the number of edges. At places where there is a~danger of confusion, the usual explicit notation
+the number of edges. At places where there could be a~danger of confusion, more explicit notation
 is used instead.