Préface
Trees are a fundamental object in graph theory and combinatorics as well as a
basic object for data structures and algorithms in computer science. During the last
few decades, research related to trees has been constantly increasing and several
algorithmic, asymptotic and probabilistic techniques have been developed in order to
study and to describe characteristics of interest related to trees in different settings.
The French School was (and still is) certainly a driving force in this development.
This is also reflected in a considerable number of research groups that devote their
research mainly to tree structures and related questions. In this context I would like
to mention Philippe Flajolet (1948–2011) who was not only the initiator of research
activities related to various tree models but was also a mentor for many researchers in
France and abroad, in particular for the authors of the present book and also for myself.
This book is a very valuable outcome of this fruitful development in France, where
the three authors have taken a very active part. They have succeeded in writing an
advanced textbook that can serve as an introduction to trees for students in mathematics
and/or computer science as well as a reference book for scientists of other fields
like biology. What is really new is that the authors present different approaches to
problems on trees that range from algorithms to combinatorics and to probability
theory. They have invested a considerable effort to demonstrate the connections and
relations between these points of view. This is a very important added value which
cannot be found somewhere else in such a transparent and consistent way.
The choice of topics is also done with care. The models are very well motivated and
range from trees that are related to branching processes, to binary search trees, to tries
and to urn models. There are also several very useful appendices and a very carefully
chosen list of exercises which make the book even more useful—also for classes. It
would be very good if an English version could be available in the near future.
I want to express my congratulations to the authors for this excellently written book.
I am sure it will develop into a standard text and reference book in the field.
Vienna, Austria
Michael Drmota
November 2016
vii
Trees are a fundamental object in graph theory and combinatorics as well as a
basic object for data structures and algorithms in computer science. During the last
few decades, research related to trees has been constantly increasing and several
algorithmic, asymptotic and probabilistic techniques have been developed in order to
study and to describe characteristics of interest related to trees in different settings.
The French School was (and still is) certainly a driving force in this development.
This is also reflected in a considerable number of research groups that devote their
research mainly to tree structures and related questions. In this context I would like
to mention Philippe Flajolet (1948–2011) who was not only the initiator of research
activities related to various tree models but was also a mentor for many researchers in
France and abroad, in particular for the authors of the present book and also for myself.
This book is a very valuable outcome of this fruitful development in France, where
the three authors have taken a very active part. They have succeeded in writing an
advanced textbook that can serve as an introduction to trees for students in mathematics
and/or computer science as well as a reference book for scientists of other fields
like biology. What is really new is that the authors present different approaches to
problems on trees that range from algorithms to combinatorics and to probability
theory. They have invested a considerable effort to demonstrate the connections and
relations between these points of view. This is a very important added value which
cannot be found somewhere else in such a transparent and consistent way.
The choice of topics is also done with care. The models are very well motivated and
range from trees that are related to branching processes, to binary search trees, to tries
and to urn models. There are also several very useful appendices and a very carefully
chosen list of exercises which make the book even more useful—also for classes. It
would be very good if an English version could be available in the near future.
I want to express my congratulations to the authors for this excellently written book.
I am sure it will develop into a standard text and reference book in the field.
Vienna, Austria
Michael Drmota
November 2016
vii