% Copyright 2008 by Till Tantau
%
% This file may be distributed and/or modified
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% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Free Documentation License.
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% See the file doc/generic/pgf/licenses/LICENSE for more details.


\section{Tutorial: A Lecture Map for Johannes}

In this tutorial we explore the tree and mind map mechanisms of
\tikzname.

Johannes is quite excited: For the first time he will be teaching a
course all by himself during the upcoming semester! Unfortunately, the
course is not on his favorite subject, which is of course Theoretical Immunology,
but on Complexity Theory, but as a young academic Johannes is not
likely to complain too loudly. In order to help the students get a
general overview of what is going to happen during the course as a
whole, he intends to draw some kind of tree or graph containing the
basic concepts. He got this idea from his old professor who seems to
be using these ``lecture maps'' with some success. Independently of
the success of these maps, Johannes thinks they look quite neat.



\subsection{Problem Statement}

Johannes wishes to create a lecture map with the following features:
\begin{enumerate}
\item It should contain a tree or graph depicting the main concepts.
\item It should somehow visualize the different lectures that will be
  taught. Note that the lectures are not necessarily the same as the
  concepts since the graph may contain more concepts than will be
  addressed in lectures and some concepts may be addressed during more
  than one lecture.
\item The map should also contain a calendar showing when the
  individual lectures will be given.
\item The aesthetical reasons, the whole map should have a visually
  nice and information-rich background.
\end{enumerate}

As always, Johannes will have to include the right libraries and
setup the environment. Since Johannes is going to use the
|mindmap| library and since he wishes to show a calendar, he will need
the |mindmap| and the |calendar| libraries. In order to put something
on a background layer, it seems like a good idea to also include the
|background| library.


\subsection{Introduction to Trees}

The first choice Johannes must make is whether he will organize the
concepts are a tree, with root concepts and concept branches and leaf
concepts, or as a general graph. The tree implicitly organizes the
concepts, while a graph is more flexible. Johannes decides to
compromise: Basically, the concepts will be organized as a
tree. However, he will selectively add connections between concepts
that are related, but which appear on different levels or branches of
the tree.

Johannes starts with a tree-like list of concepts that he feels are
important in Computational Complexity:

\begin{itemize}
\item Computational Problems
  \begin{itemize}\itemsep=0pt\parskip=0pt
  \item Problem Measures
  \item Problem Aspects
  \item Problem Domains
  \item Key Problems
  \end{itemize}
\item Computational Models
  \begin{itemize}\itemsep=0pt\parskip=0pt
  \item Turing Machines
  \item Random-Access Machines
  \item Circuits
  \item Binary Decision Diagrams
  \item Oracle Machines
  \item Programming in Logic
  \end{itemize}
\item Measuring Complexity
  \begin{itemize}\itemsep=0pt\parskip=0pt
  \item Complexity Measures
  \item Classifying Complexity
  \item Comparing Complexity
  \item Describing Complexity
  \end{itemize}
\item Solving Problems
  \begin{itemize}\itemsep=0pt\parskip=0pt
  \item Exact Algorithms
  \item Randomization
  \item Fixed-Parameter Algorithms
  \item Parallel Computation
  \item Partial Solutions
  \item Approximation
  \end{itemize}
\end{itemize}

Johannes will surely need to modify this list later on, but it looks
good as a first approximation. He will also need to add a number of
subtopics (like \emph{lots} of complexity classes under the topic
``classifying complexity''), but he will do this as he constructs the
map. 

Turning the list of topics into a \tikzname-tree is easy, in
principle. The basic idea is that a node can have \emph{children},
which in turn can have children of their own, and so on. To add a
child to a node, Johannes can simply write |child {|\meta{node}|}|
right after a node. The \meta{node} should, in turn, be the code for
creating a node. To add another node, Johannes can use |child| once
more, and so on. Johannes is eager to try out this construct and
writes down the following:

\begin{codeexample}[]
\tikz
  \node {Computational Complexity} % root
    child { node {Computational Problems}
      child { node {Problem Measures} }
      child { node {Problem Aspects} }
      child { node {Problem Domains} }
      child { node {Key Problems} }
    }
    child { node {Computational Models}
      child { node {Turing Machines} }
      child { node {Random-Access Machines} }
      child { node {Circuits} }
      child { node {Binary Decision Diagrams} }
      child { node {Oracle Machines} }
      child { node {Programming in Logic} }
    }
    child { node {Measuring Complexity} 
      child { node {Complexity Measures} }
      child { node {Classifying Complexity} }
      child { node {Comparing Complexity} }
      child { node {Describing Complexity} }
    }
    child { node {Solving Problems}
      child { node {Exact Algorithms} }
      child { node {Randomization} }
      child { node {Fixed-Parameter Algorithms} }
      child { node {Parallel Computation} }
      child { node {Partial Solutions} }
      child { node {Approximation} }
    };    
\end{codeexample}

Well, that did not quite work out as expected (although, what,
exactly, did one expect?). There are two problems:
\begin{enumerate}
\item The overlap of the nodes is due to the fact that \tikzname\ is
  not particularly smart when it comes to placing child nodes. Even
  though it is possible to configure \tikzname\ to use rather clever
  placement methods, \tikzname\ has no way of taking the actual size
  of the child nodes into account. This may seem strange but the
  reason is that the child nodes are rendered and placed one at a
  time, so the size of the last node is not known when the first node
  is being processed. In essence, you have to specify appropriate
  level and sibling node spacings ``by hand.''
\item The standard computer-science-top-down rendering of a tree is
  rather ill-suited to visualizing the concepts. It would be better to
  either rotate the map by ninety degrees or, even better, to use some
  sort of circular arrangement.
\end{enumerate}

Johannes redraws the tree, but this time with some more appropriate
options set, which he found more or less by trial-and-error:

\begin{codeexample}[render instead={
\tikz [font=\footnotesize,
       grow=right, level 1/.style={sibling distance=6em},
                   level 2/.style={sibling distance=1em}, level distance=5cm]
  \node {Computational Complexity} % root
    child { node {Computational Problems}
      child { node {Problem Measures} }           child { node {Problem Aspects} }
      child { node {Problem Domains} }            child { node {Key Problems} }
    }
    child { node {Computational Models}
      child { node {Turing Machines} }            child { node {Random-Access Machines} }
      child { node {Circuits} }                   child { node {Binary Decision Diagrams} }
      child { node {Oracle Machines} }            child { node {Programming in Logic} }
    }
    child { node {Measuring Complexity} 
      child { node {Complexity Measures} }        child { node {Classifying Complexity} }
      child { node {Comparing Complexity} }       child { node {Describing Complexity} }
    }
    child { node {Solving Problems}
      child { node {Exact Algorithms} }           child { node {Randomization} }
      child { node {Fixed-Parameter Algorithms} } child { node {Parallel Computation} }
      child { node {Partial Solutions} }          child { node {Approximation} }
    };    
    }]
\tikz [font=\footnotesize,
       grow=right, level 1/.style={sibling distance=6em},
                   level 2/.style={sibling distance=1em}, level distance=5cm]
  \node {Computational Complexity} % root
    child { node {Computational Problems}
      child { node {Problem Measures} }
      child { node {Problem Aspects} }
      ... % as before
\end{codeexample}

Still not quite what Johannes had in mind, but he is getting
somewhere.

For configuring the tree, two parameters are of particular importance:
The |level distance| tells \tikzname\ the distance between (the
centers of) the nodes on adjacent levels or layers of a tree. The
|sibling distance| is, as the name suggests, the distance between (the
centers of) siblings of the tree. 

You can globally set these parameters for a tree by simply setting
them somewhere before the tree starts, but you will
typically wish them to be different for different levels of the
tree. In this case, you should set styles like |level 1| or
|level 2|. For the first level of the tree, the |level 1| style is
used, for the second level the |level 2| style, and so on. You can
also set the sibling and level distances only for certain nodes by
passing these options to the |child| command as options. (Note that
the options of a |node| command are local to the node and have no
effect on the children. Also note that it is possible to specify
options that do have an effect on the children. Finally note that
specifying options for children ``at the right place'' is an arcane
art and you should peruse Section~\ref{section-tree-options} on 
a rainy Sunday afternoon, if you are really interested.)

The |grow| key is used to configure the direction in which a tree
grows. You can change growth direction ``in the middle of a tree''
simply by changing this key for a single child or a whole level. By
including the |tree| library you also get access to additional growth
strategies such as a ``circular'' growth:


\begin{codeexample}[render instead={
\tikz [text width=2.7cm, align=flush center,
       grow cyclic, 
       level 1/.style={level distance=2.5cm,sibling angle=90},
       level 2/.style={text width=2cm, font=\footnotesize, level distance=3cm,sibling angle=30}]
  \node[font=\bfseries] {Computational Complexity} % root
    child { node {Computational Problems}
      child { node {Problem Measures} }           child { node {Problem Aspects} }
      child { node {Problem Domains} }            child { node {Key Problems} }
    }
    child { node {Computational Models}
      child { node {Turing Machines} }            child { node {Random-Access Machines} }
      child { node {Circuits} }                   child { node {Binary Decision Diagrams} }
      child { node {Oracle Machines} }            child { node {Programming in Logic} }
    }
    child { node {Measuring Complexity} 
      child { node {Complexity Measures} }        child { node {Classifying Complexity} }
      child { node {Comparing Complexity} }       child { node {Describing Complexity} }
    }
    child { node {Solving Problems}
      child { node {Exact Algorithms} }           child { node {Randomization} }
      child { node {Fixed-Parameter Algorithms} } child { node {Parallel Computation} }
      child { node {Partial Solutions} }          child { node {Approximation} }
    };    
    }]
\tikz [text width=2.7cm, align=flush center,
       grow cyclic, 
       level 1/.style={level distance=2.5cm,sibling angle=90},
       level 2/.style={text width=2cm, font=\footnotesize, level distance=3cm,sibling angle=30}]
  \node[font=\bfseries] {Computational Complexity} % root
    child { node {Computational Problems}
      child { node {Problem Measures} }
      child { node {Problem Aspects} }
      ... % as before
\end{codeexample}


Johannes is pleased to learn that he can access and manipulate the
nodes of tree like any normal node. In particular, he can name them
using the |name=| option or the |(|\meta{name}|)| notation and he can
use any available shape or style for the trees nodes. He can connect
trees later on using the normal |\draw (some node) -- (another node);|
syntax. In essence, the |child| command just computes an appropriate
position for a node and adds a line from the child to the parent
node. 


\subsection{Creating the Lecture Map}

Johannes now has a first possible layout for his lecture map. The next
step is to make it ``look nicer.'' For this, the |mindmap| library is
helpful since it makes a number of styles available that will make a
tree look like a nice ``mind map'' or ``concept map.''

The first step is to include the |mindmap| library, which Johannes
already did. Next, he must add one of the following options to a scope
that will contain the lecture map: |mindmap| or |large mindmap| or
|huge mindmap|. These options all have the same effect, except that
for a |large mindmap| the predefined font size and node sizes are
somewhat larger than for a standard |mindmap| and for a |huge mindmap|
they are even larger. So, a |large mindmap| does not necessarily need
to have a lot of concepts, but it will need a lot of paper.

The second step is to add the |concept| option to every node that
will, indeed, be a concept of the mindmap. The idea is that some nodes
of a tree will be real concepts, while other nodes might just be
``simple children.'' Typically, this is not the case, so you might
consider saying |every node/.style=concept|.

The third step is to setup the sibling \emph{angle} (rather than a
sibling distance) to specify the angle between sibling concepts.

\begin{codeexample}[render instead={
\tikz [mindmap, every node/.style=concept, concept color=black!20,
       grow cyclic, 
       level 1/.append style={level distance=4.5cm,sibling angle=90},
       level 2/.append style={level distance=3cm,sibling angle=45}]
  \node [root concept] {Computational Complexity} % root
    child { node {\hbox to 2cm{Computational\hss} Problems}
      child { node {Problem Measures} }
      child { node {Problem Aspects} }
      child { node {Problem Domains} }
      child { node {Key Problems} }
    }
    child { node {\hbox to 2cm{Computational\hss} Models}
      child { node {Turing Machines} }
      child { node {Random-Access Machines} }
      child { node {Circuits} }
      child { node {Binary Decision Diagrams} }
      child { node {Oracle Machines} }
      child { node {\hbox to1.5cm{Programming\hss} in Logic} }
    }
    child { node {Measuring Complexity} 
      child { node {Complexity Measures} }
      child { node {Classifying Complexity} }
      child { node {Comparing Complexity} }
      child { node {Describing Complexity} }
    }
    child { node {Solving Problems}
      child { node {Exact Algorithms} }
      child { node {\hbox to 1.5cm{Randomization\hss}} }
      child { node {Fixed-Parameter Algorithms} }
      child { node {Parallel Computation} }
      child { node {Partial Solutions} }
      child { node {\hbox to1.5cm{Approximation\hss}} }
    };}]
\tikz [mindmap, every node/.style=concept, concept color=black!20,
       grow cyclic, 
       level 1/.append style={level distance=4.5cm,sibling angle=90},
       level 2/.append style={level distance=3cm,sibling angle=45}]
  \node [root concept] {Computational Complexity} % root
    child { node {Computational Problems}
      child { node {Problem Measures} }
      child { node {Problem Aspects} }
      ... % as before
\end{codeexample}

When Johannes typesets the above map, \TeX\ (rightfully) starts
complaining about several overfull boxes and, indeed, words like
``Randomization'' stretch out beyond the circle of the concept. This
seems a bit mysterious at first sight: Why does \TeX\ not hyphenate
the word? The reason is that \TeX\ will never hyphenate the first word
of a paragraph because it starts looking for ``hyphenatable'' letters
only after a so-called glue. In order to have \TeX\ hyphenate these
single words, Johannes must use a bit of evil trickery: He inserts a
|\hskip0pt| before the word. This has no effect except for inserting
an (invisible) glue before the word and, thereby, allowing \TeX\ to
hyphenate the first word also. Since Johannes does not want to add
|\hskip0pt| inside each node, he uses the |execute at begin node|
option to make \tikzname\ insert this text with every node.


\begin{codeexample}[render instead={
\begin{tikzpicture}
  [mindmap,
   every node/.style={concept, execute at begin node=\hskip0pt},
   concept color=black!20,
   grow cyclic, 
   level 1/.append style={level distance=4.5cm,sibling angle=90},
   level 2/.append style={level distance=3cm,sibling angle=45}]
  \clip (-1,2) rectangle ++ (-4,5);
  \node [root concept] {Computational Complexity} % root
    child { node {Computational Problems}
      child { node {Problem Measures} }
      child { node {Problem Aspects} }
      child { node {Problem Domains} }
      child { node {Key Problems} }
    }
    child { node {Computational Models}
      child { node {Turing Machines} }
      child { node {Random-Access Machines} }
      child { node {Circuits} }
      child { node {Binary Decision Diagrams} }
      child { node {Oracle Machines} }
      child { node {Programming in Logic} }
    }
    child { node {Measuring Complexity} 
      child { node {Complexity Measures} }
      child { node {Classifying Complexity} }
      child { node {Comparing Complexity} }
      child { node {Describing Complexity} }
    }
    child { node {Solving Problems}
      child { node {Exact Algorithms} }
      child { node {Randomization} }
      child { node {Fixed-Parameter Algorithms} }
      child { node {Parallel Computation} }
      child { node {Partial Solutions} }
      child { node {Approximation} }
    };
\end{tikzpicture}
}]
\begin{tikzpicture}
  [mindmap,
   every node/.style={concept, execute at begin node=\hskip0pt},
   concept color=black!20,
   grow cyclic, 
   level 1/.append style={level distance=4.5cm,sibling angle=90},
   level 2/.append style={level distance=3cm,sibling angle=45}]
  \clip (-1,2) rectangle ++ (-4,5);
  \node [root concept] {Computational Complexity} % root
    child { node {Computational Problems}
      child { node {Problem Measures} }
      child { node {Problem Aspects} }
      ... % as before
\end{tikzpicture}
\end{codeexample}


In the above example a clipping was used to show only part of the
lecture map, in order to save space. The same will be done in the
following examples, we return to the complete lecture map at the end of this
tutorial.

Johannes is now eager to colorize the map. The idea is to use
different colors for different parts of the map. He can then, during
his lectures, talk about the ``green'' or the ``red'' topics. This
will make it easier for his students to locate the topic he is talking
about on the map. Since ``computational problems'' somehow sounds
``problematic,'' Johannes chooses red for them, while he picks green
for the ``solving problems.'' The topics ``measuring complexity'' and
``computational models'' get more neutral colors; Johannes picks
orange and blue.

To set the colors, Johannes must use the |concept color| option,
rather than just, say, |node [fill=red]|. Setting just the fill color
to |red| would, indeed, make the node red, but it would \emph{just}
make the node red and not the bar connecting the concept to its parent
and also not its children. By comparison, the special |concept color|
option will not only set the color of the node and its children, but
it will also (magically) create appropriate shadings so that the color
of a parent concept smoothly changes to the color of a child concept.

For the root concept Johannes decides to do something special: He sets
the concept color to black, sets the line width to a large value, and
sets the fill color to white. The effect of this is that the root
concept will encircled with a thick black line and the children are
connected to the central concept via bars.

\begin{codeexample}[render instead={
\begin{tikzpicture}
  [mindmap,
   every node/.style={concept, execute at begin node=\hskip0pt},
   root concept/.append style={
     concept color=black,
     fill=white, line width=1ex,
     text=black},
   text=white,
   grow cyclic,
   level 1/.append style={level distance=4.5cm,sibling angle=90},
   level 2/.append style={level distance=3cm,sibling angle=45}]
  \clip (0,-1) rectangle ++(4,5);
  \node [root concept] {Computational Complexity} % root
    child [concept color=red] { node {Computational Problems}
      child { node {Problem Measures} }
      child { node {Problem Aspects} }
      child { node {Problem Domains} }
      child { node {Key Problems} }
    }
    child [concept color=blue] { node {Computational Models}
      child { node {Turing Machines} }
      child { node {Random-Access Machines} }
      child { node {Circuits} }
      child { node {Binary Decision Diagrams} }
      child { node {Oracle Machines} }
      child { node {Programming in Logic} }
    }
    child [concept color=orange] { node {Measuring Complexity} 
      child { node {Complexity Measures} }
      child { node {Classifying Complexity} }
      child { node {Comparing Complexity} }
      child { node {Describing Complexity} }
    }
    child [concept color=green!50!black] { node {Solving Problems}
      child { node {Exact Algorithms} }
      child { node {Randomization} }
      child { node {Fixed-Parameter Algorithms} }
      child { node {Parallel Computation} }
      child { node {Partial Solutions} }
      child { node {Approximation} }
    };
  \end{tikzpicture}}]
\begin{tikzpicture}
  [mindmap,
   every node/.style={concept, execute at begin node=\hskip0pt},
   root concept/.append style={
     concept color=black, fill=white, line width=1ex, text=black},
   text=white,
   grow cyclic,
   level 1/.append style={level distance=4.5cm,sibling angle=90},
   level 2/.append style={level distance=3cm,sibling angle=45}]
   \clip (0,-1) rectangle ++(4,5);
  \node [root concept] {Computational Complexity} % root
    child [concept color=red] { node {Computational Problems}
      child { node {Problem Measures} }
      ... % as before
    }
    child [concept color=blue] { node {Computational Models}
      child { node {Turing Machines} }
      ... % as before
    }
    child [concept color=orange] { node {Measuring Complexity} 
      child { node {Complexity Measures} }
      ... % as before
    }
    child [concept color=green!50!black] { node {Solving Problems}
      child { node {Exact Algorithms} }
      ... % as before
    };
\end{tikzpicture}
\end{codeexample}

Johannes adds three finishing touches: First, he changes the font
of the main concepts to small caps. Second, he decides that some
concepts should be ``faded,'' namely those that are important in
principle and belong on the map, but which he will not talk about in
his lecture. To achieve this, Johannes defines four styles, one for
each of the four main branches. These styles (a) setup the
correct concept color for the whole branch and (b) define the |faded|
style appropriately for this branch. Third, he adds a
|circular drop shadow|, defined in the |shadows| library, to the
concepts, just to make things look a bit more fancy. 

\begin{codeexample}[render instead={
\begin{tikzpicture}[mindmap]
  \begin{scope}[      
   every node/.style={concept, circular drop shadow,execute at begin node=\hskip0pt},
   root concept/.append style={
     concept color=black,
     fill=white, line width=1ex,
     text=black, font=\large\scshape},
   text=white,
   computational problems/.style={concept color=red,faded/.style={concept color=red!50}},
   computational models/.style={concept color=blue,faded/.style={concept color=blue!50}},
   measuring complexity/.style={concept color=orange,faded/.style={concept color=orange!50}},
   solving problems/.style={concept color=green!50!black,faded/.style={concept color=green!50!black!50}},
   grow cyclic,
   level 1/.append style={level distance=4.5cm,sibling angle=90,font=\scshape},
   level 2/.append style={level distance=3cm,sibling angle=45,font=\scriptsize}]
  \node [root concept] {Computational Complexity} % root
    child [computational problems] { node {Computational Problems}
      child         { node {Problem Measures} }
      child         { node {Problem Aspects} }
      child [faded] { node {Problem Domains} }
      child         { node {Key Problems} }
    }
    child [computational models] { node {Computational Models}
      child         { node {Turing Machines} }
      child [faded] { node {Random-Access Machines} }
      child         { node {Circuits} }
      child [faded] { node {Binary Decision Diagrams} }
      child         { node {Oracle Machines} }
      child         { node {Programming in Logic} }
    }
    child [measuring complexity] { node {Measuring Complexity} 
      child         { node {Complexity Measures} }
      child         { node {Classifying Complexity} }
      child         { node {Comparing Complexity} }
      child [faded] { node {Describing Complexity} }
    }
    child [solving problems] { node {Solving Problems}
      child         { node {Exact Algorithms} }
      child         { node {Randomization} }
      child         { node {Fixed-Parameter Algorithms} }
      child         { node {Parallel Computation} }
      child         { node {Partial Solutions} }
      child         { node {Approximation} }
    };
  \end{scope}
\end{tikzpicture}}]
\begin{tikzpicture}[mindmap]
  \begin{scope}[
    every node/.style={concept, circular drop shadow,execute at begin node=\hskip0pt},
    root concept/.append style={
      concept color=black, fill=white, line width=1ex, text=black, font=\large\scshape},
    text=white,
    computational problems/.style={concept color=red,faded/.style={concept color=red!50}},
    computational models/.style={concept color=blue,faded/.style={concept color=blue!50}},
    measuring complexity/.style={concept color=orange,faded/.style={concept color=orange!50}},
    solving problems/.style={concept color=green!50!black,faded/.style={concept color=green!50!black!50}},
    grow cyclic,
    level 1/.append style={level distance=4.5cm,sibling angle=90,font=\scshape},
    level 2/.append style={level distance=3cm,sibling angle=45,font=\scriptsize}]
    \node [root concept] {Computational Complexity} % root
      child [computational problems] { node {Computational Problems}
        child         { node {Problem Measures} }
        child         { node {Problem Aspects} }
        child [faded] { node {Problem Domains} }
        child         { node {Key Problems} }
      }
      child [computational models] { node {Computational Models}
        child         { node {Turing Machines} }
        child [faded] { node {Random-Access Machines} }
        ...
  \end{scope}
\end{tikzpicture}
\end{codeexample}


\subsection{Adding the Lecture Annotations}

Johannes will give about a dozen lectures during the course
``computational complexity.'' For each lecture he has compiled a
(short) list of learning targets that state what knowledge and
qualifications his students should acquire during this particular
lecture (note that learning targets are not the same as the contents
of a lecture). For each lecture he intends to put a little rectangle
on the map containing these learning targets and the name of the
lecture, each time somewhere near to the topic of the lecture. Such
``little rectangles'' are called ``annotations'' by the mindmap
library. 

In order to place the annotations next to the concepts, Johannes must
assign names to the nodes of the concepts. He could rely on
\tikzname's automatic naming of the nodes in a tree, where the
children of a node named |root| are named |root-1|, |root-2|,
|root-3|, and so on. However, since Johannes is not sure about the
final order of the concepts in the tree, it seems better to explicitly
name all concepts of the tree in the following manner:

\begin{codeexample}[code only]
\node [root concept] (Computational Complexity) {Computational Complexity} 
  child [computational problems] { node (Computational Problems) {Computational Problems}
    child         { node (Problem Measures) {Problem Measures} }
    child         { node (Problem Aspects) {Problem Aspects} }
    child [faded] { node (Problem Domains) {Problem Domains} }
    child         { node (Key Problems) {Key Problems} }
  }
...
\end{codeexample}

The |annotation| style of the mind map library mainly sets up a
rectangular shape of appropriate size. Johannes configures the style
by defining |every annotation| appropriately.

\begin{codeexample}[render instead={
\begin{tikzpicture}[mindmap]
  \clip (-5.25,-3) rectangle ++ (4,5);
  \begin{scope}[
    every node/.style={concept, circular drop shadow,execute at begin node=\hskip0pt},
    root concept/.append style={
      concept color=black,
      fill=white, line width=1ex,
      text=black, font=\large\scshape},
    text=white,
    computational problems/.style={concept color=red,faded/.style={concept color=red!50}},
    computational models/.style={concept color=blue,faded/.style={concept color=blue!50}},
    measuring complexity/.style={concept color=orange,faded/.style={concept color=orange!50}},
    solving problems/.style={concept color=green!50!black,faded/.style={concept color=green!50!black!50}},
    grow cyclic,
    level 1/.append style={level distance=4.5cm,sibling angle=90,font=\scshape},
    level 2/.append style={level distance=3cm,sibling angle=45,font=\scriptsize}]
    \node [root concept] (Computational Complexity) {Computational Complexity} % root
      child [computational problems] { node (Computational Problems) {Computational Problems}
        child         { node (Problem Measures) {Problem Measures} }
        child         { node (Problem Aspects) {Problem Aspects} }
        child [faded] { node (problem Domains) {Problem Domains} }
        child         { node (Key Problems) {Key Problems} }
      }
      child [computational models] { node (Computational Models) {Computational Models}
        child         { node (Turing Machines) {Turing Machines} }
        child [faded] { node (Random-Access Machines) {Random-Access Machines} }
        child         { node (Circuits) {Circuits} }
        child [faded] { node (Binary Decision Diagrams) {Binary Decision Diagrams} }
        child         { node (Oracle Machines) {Oracle Machines} }
        child         { node (Programming in Logic) {Programming in Logic} }
      }
      child [measuring complexity] { node (Measuring Complexity) {Measuring Complexity} 
        child         { node (Complexity Measures) {Complexity Measures} }
        child         { node (Classifying Complexity) {Classifying Complexity} }
        child         { node (Comparing Complexity) {Comparing Complexity} }
        child [faded] { node (Describing Complexity) {Describing Complexity} }
      }
      child [solving problems] { node (Solving Problems) {Solving Problems}
        child         { node (Exact Algorithms) {Exact Algorithms} }
        child         { node (Randomization) {Randomization} }
        child         { node (Fixed-Parameter Algorithms) {Fixed-Parameter Algorithms} }
        child         { node (Parallel Computation) {Parallel Computation} }
        child         { node (Partial Solutions) {Partial Solutions} }
        child         { node (Approximation) {Approximation} }
      };
  \end{scope}
  \begin{scope}[every annotation/.style={fill=black!40}]
    \node [annotation, above] at (Computational Problems.north) {
      Lecture 1: Computational Problems
      \begin{itemize}
      \item Knowledge of several key problems
      \item Knowledge of problem encondings
      \item Being able to formalize problems
      \end{itemize}
    };
  \end{scope}
\end{tikzpicture}}]
\begin{tikzpicture}[mindmap]
  \clip (-5,-5) rectangle ++ (4,5);
  \begin{scope}[
     every node/.style={concept, circular drop shadow, ...] % as before
    \node [root concept] (Computational Complexity)    ... % as before
  \end{scope}
  
  \begin{scope}[every annotation/.style={fill=black!40}]
    \node [annotation, above] at (Computational Problems.north) {
      Lecture 1: Computational Problems
      \begin{itemize}
      \item Knowledge of several key problems
      \item Knowledge of problem encondings
      \item Being able to formalize problems
      \end{itemize}
    };
  \end{scope}
\end{tikzpicture}        
\end{codeexample}

Well, that does not yet look quite perfect. The spacing or the
|{itemize}| is not really appropriate and the node is too
large. Johannes can configure these things ``by hand,'' but it seems
like a good idea to define a macro that will take care of these things
for him. The ``right'' way to do this is to define a |\lecture| macro
that takes a list of key-value pairs as argument and produces the
desired annotation. However, to keep things simple, Johannes'
|\lecture| macro simply takes a fixed number of arguments having the
following meaning: The first argument is the number of the lecture,
the second is the name of the lecture, the third are positioning
options like |above|, the fourth is the position where the node is
placed, the fifth is the list of items to be shown, and the sixth is a
date when the lecture will be held (this parameter is not yet needed,
we will, however, need it later on).

\begin{codeexample}[code only]
\def\lecture#1#2#3#4#5#6{
  \node [annotation, #3, scale=0.65, text width=4cm, inner sep=2mm] at (#4) {
    Lecture #1: \textcolor{orange}{\textbf{#2}}
    \list{--}{\topsep=2pt\itemsep=0pt\parsep=0pt
              \parskip=0pt\labelwidth=8pt\leftmargin=8pt
              \itemindent=0pt\labelsep=2pt}
    #5
    \endlist
  };
}
\end{codeexample}
\def\lecture#1#2#3#4#5#6{
  \node [annotation, #3, scale=0.65, text width=4cm, inner sep=2mm] at (#4) {
    Lecture #1: \textcolor{orange}{\textbf{#2}}
    \list{--}{\topsep=2pt\itemsep=0pt\parsep=0pt
              \parskip=0pt\labelwidth=8pt\leftmargin=8pt
              \itemindent=0pt\labelsep=2pt}
    #5
    \endlist
  };
}

\begin{codeexample}[render instead={
\begin{tikzpicture}[mindmap,every annotation/.style={fill=white}]
  \clip (-5.25,-3) rectangle ++ (4,5);
  \begin{scope}[
    every node/.style={concept, circular drop shadow,execute at begin node=\hskip0pt},
    root concept/.append style={
      concept color=black,
      fill=white, line width=1ex,
      text=black, font=\large\scshape},
    text=white,
    computational problems/.style={concept color=red,faded/.style={concept color=red!50}},
    computational models/.style={concept color=blue,faded/.style={concept color=blue!50}},
    measuring complexity/.style={concept color=orange,faded/.style={concept color=orange!50}},
    solving problems/.style={concept color=green!50!black,faded/.style={concept color=green!50!black!50}},
    grow cyclic,
    level 1/.append style={level distance=4.5cm,sibling angle=90,font=\scshape},
    level 2/.append style={level distance=3cm,sibling angle=45,font=\scriptsize}]
    \node [root concept] (Computational Complexity) {Computational Complexity} % root
      child [computational problems] { node (Computational Problems) {Computational Problems}
        child         { node (Problem Measures) {Problem Measures} }
        child         { node (Problem Aspects) {Problem Aspects} }
        child [faded] { node (problem Domains) {Problem Domains} }
        child         { node (Key Problems) {Key Problems} }
      }
      child [computational models] { node (Computational Models) {Computational Models}
        child         { node (Turing Machines) {Turing Machines} }
        child [faded] { node (Random-Access Machines) {Random-Access Machines} }
        child         { node (Circuits) {Circuits} }
        child [faded] { node (Binary Decision Diagrams) {Binary Decision Diagrams} }
        child         { node (Oracle Machines) {Oracle Machines} }
        child         { node (Programming in Logic) {Programming in Logic} }
      }
      child [measuring complexity] { node (Measuring Complexity) {Measuring Complexity} 
        child         { node (Complexity Measures) {Complexity Measures} }
        child         { node (Classifying Complexity) {Classifying Complexity} }
        child         { node (Comparing Complexity) {Comparing Complexity} }
        child [faded] { node (Describing Complexity) {Describing Complexity} }
      }
      child [solving problems] { node (Solving Problems) {Solving Problems}
        child         { node (Exact Algorithms) {Exact Algorithms} }
        child         { node (Randomization) {Randomization} }
        child         { node (Fixed-Parameter Algorithms) {Fixed-Parameter Algorithms} }
        child         { node (Parallel Computation) {Parallel Computation} }
        child         { node (Partial Solutions) {Partial Solutions} }
        child         { node (Approximation) {Approximation} }
      };
  \end{scope}
  \lecture{1}{Computational Problems}{above,xshift=-3mm}{Computational Problems.north}{
    \item Knowledge of several key problems
    \item Knowledge of problem encondings
    \item Being able to formalize problems
  }{2009-04-08}
\end{tikzpicture}}]
\begin{tikzpicture}[mindmap,every annotation/.style={fill=white}]
  \clip (-5,-5) rectangle ++ (4,5);
  \begin{scope}[
     every node/.style={concept, circular drop shadow, ... % as before
    \node [root concept] (Computational Complexity)    ... % as before
  \end{scope}
  
  \lecture{1}{Computational Problems}{above,xshift=-3mm}
  {Computational Problems.north}{
    \item Knowledge of several key problems
    \item Knowledge of problem encondings
    \item Being able to formalize problems
  }{2009-04-08}
\end{tikzpicture}        
\end{codeexample}

In the same fashion Johannes can now add the other lecture
annotations. Obviously, Johannes will have some trouble fitting
everything on a single A4-sized page, but by adjusting the spacing and
some experimentation he can quickly arrange all the annotations as needed.


\subsection{Adding the Background}

Johannes has already used colors to organize his lecture map into four
regions, each having a different color. In order to emphasize these
regions even more strongly, he wishes to add a background coloring to
each of these regions.

Adding these background colors turns out to be more tricky than
Johannes would have thought. At first sight, what he needs is some
sort of ``color wheel'' that is blue in the lower right direction and
then changes smoothly to orange in the upper right direction and then
to green in the upper left direction and so on. Unfortunately, there
is no easy way of creating a true such a color wheel shading (although
it can be done, in principle, but only at a very high cost, see
page~\pageref{shading-color-wheel} for an example).

Johannes decides to do something a bit more basic: He creates four
large rectangles, one for each of the four quadrants around the
central concept, each colored with a light version of the
quadrant. Then, in order to ``smooth'' the change between adjacent
rectangles, he puts four shadings on top of them.

Since these background rectangles should go ``behind'' everything
else, Johannes puts all his background stuff on the |background|
layer.

In the following code, only the central concept is shown to save some
space:
\begin{codeexample}[]
\begin{tikzpicture}[
  mindmap,
  concept color=black,
  root concept/.append style={
    concept,
    circular drop shadow,
    fill=white, line width=1ex,
    text=black, font=\large\scshape}
  ]

  \clip (-1.5,-5) rectangle ++(4,10);

  \node [root concept] (Computational Complexity) {Computational Complexity};
  
  \begin{pgfonlayer}{background}
    \clip (-1.5,-5) rectangle ++(4,10);
    
    \colorlet{upperleft}{green!50!black!25}
    \colorlet{upperright}{orange!25}
    \colorlet{lowerleft}{red!25}
    \colorlet{lowerright}{blue!25}

     % The large rectangles:
    \fill [upperleft]  (Computational Complexity) rectangle ++(-20,20);
    \fill [upperright] (Computational Complexity) rectangle ++(20,20);
    \fill [lowerleft]  (Computational Complexity) rectangle ++(-20,-20);
    \fill [lowerright] (Computational Complexity) rectangle ++(20,-20);

    % The shadings:
    \shade [left color=upperleft,right color=upperright]
      ([xshift=-1cm]Computational Complexity) rectangle ++(2,20);
    \shade [left color=lowerleft,right color=lowerright]
      ([xshift=-1cm]Computational Complexity) rectangle ++(2,-20);
    \shade [top color=upperleft,bottom color=lowerleft]
      ([yshift=-1cm]Computational Complexity) rectangle ++(-20,2);
    \shade [top color=upperright,bottom color=lowerright]
      ([yshift=-1cm]Computational Complexity) rectangle ++(20,2);
  \end{pgfonlayer}
\end{tikzpicture}
\end{codeexample}



\subsection{Adding the Calendar}

Johannes intends to plan his lecture rather carefully. In particular,
he already knows when each of his lectures will be held during the
course. Naturally, this does not mean that Johannes will slavishly
follow the plan and he might need longer for some subjects than he
anticipated, but nevertheless he has a detailed plan of when which
subject will be addressed.

Johannes intends to share this plan with his students by adding a
calendar to the lecture map. In addition to serving as a reference
on which particular day a certain  topic will be addressed, the
calendar is also useful so show the overall chronological order of the
course.

In order to add a calendar to a \tikzname\ graphic, the |calendar|
library is most useful. The library provides the |\calendar| command,
which takes a large number of options and which can be configured in
many ways to produce just about any kind of calendar imaginable. For
Johannes' purposes, a simple |day list downward| will be a nice option
since it produces a list of days that go ``downward''.

\begin{codeexample}[leave comments]
\tiny
\begin{tikzpicture}
  \calendar [day list downward,
             name=cal,
             dates=2009-04-01 to 2009-04-14]
    if (weekend)
      [black!25];
\end{tikzpicture}
\end{codeexample}

Using the |name| option, we gave a name to the calendar, which will
allow us to reference the nodes that make up the individual days of
the calendar later on. For instance, the rectangular node containing the
|1| that represents April 1st, 2009, can be referenced as
|(cal-2009-04-01)|. The |dates| option is used to specify an 
interval for which the calendar should be drawn. Johannes will need
several months in his calendar, but the above example only shows two
weeks to save some space.

Note the |if (weekend)| construct. The |\calendar| command is followed
by options and then by |if|-statements. These |if|-statements are
checked for each day of the calendar and when a date passes this test,
the options or the code following the |if|-statement is executed. In
the above example, we make weekend days (Saturdays and Sundays, to be
precise) lighter than normal days. (Use your favorite calendar to
check that, indeed, April 5th, 2009, is a Sunday.)

As mentioned above, Johannes can reference the nodes that are used to
typeset days. Recall that his |\lecture| macro already got passed a
date, which we did not use, yet. We can now use it to place the
lecture's title next to the date when the lecture will be held:


\begin{codeexample}[code only]
\def\lecture#1#2#3#4#5#6{
  % As before:    
  \node [annotation, #3, scale=0.65, text width=4cm, inner sep=2mm] at (#4) {
    Lecture #1: \textcolor{orange}{\textbf{#2}}
    \list{--}{\topsep=2pt\itemsep=0pt\parsep=0pt
              \parskip=0pt\labelwidth=8pt\leftmargin=8pt
              \itemindent=0pt\labelsep=2pt}
    #5
    \endlist
  };
  % New:
  \node [anchor=base west] at (cal-#6.base east) {\textcolor{orange}{\textbf{#2}}};
}
\end{codeexample}
\def\lecture#1#2#3#4#5#6{
  \node [anchor=base west] at (cal-#6.base east) {\textcolor{orange}{\textbf{#2}}};
}

Johannes can now use this new |\lecture| command as follows (in the
example, only the new part of the definition is used):

\begin{codeexample}[]
\tiny
\begin{tikzpicture}
  \calendar [day list downward,
             name=cal,
             dates=2009-04-01 to 2009-04-14]
    if (weekend)
      [black!25];

  % As before:
  \lecture{1}{Computational Problems}{above,xshift=-3mm}
  {Computational Problems.north}{
    \item Knowledge of several key problems
    \item Knowledge of problem encondings
    \item Being able to formalize problems
  }{2009-04-08}      
\end{tikzpicture}
\end{codeexample}


As a final step, Johannes needs to add a few more options to the
calendar command: He uses the |month text| option to configure how the
text of a month is rendered (see Section~\ref{section-calender} for
details) and then typesets the month text at a special position at the
beginning of each month.
    
\begin{codeexample}[leave comments]
\tiny
\begin{tikzpicture}
  \calendar [day list downward,
             month text=\%mt\ \%y0,
             month yshift=3.5em,
             name=cal,
             dates=2009-04-01 to 2009-05-01]
    if (weekend)
      [black!25]
    if (day of month=1) {
      \node at (0pt,1.5em) [anchor=base west] {\small\tikzmonthtext};
    };
    
  \lecture{1}{Computational Problems}{above,xshift=-3mm}
  {Computational Problems.north}{
    \item Knowledge of several key problems
    \item Knowledge of problem encondings
    \item Being able to formalize problems
  }{2009-04-08}      
    
  \lecture{2}{Computational Models}{above,xshift=-3mm}
  {Computational Models.north}{
    \item Knowledge of Turing machines
    \item Being able to compare the computational power of different
      models 
  }{2009-04-15}      
\end{tikzpicture}
\end{codeexample}



\subsection{The Complete Code}

Putting it all together, Johannes gets the following code:

First comes the definition of the |\lecture| command:

\begin{codeexample}[code only]
\def\lecture#1#2#3#4#5#6{
  % As before:    
  \node [annotation, #3, scale=0.65, text width=4cm, inner sep=2mm, fill=white] at (#4) {
    Lecture #1: \textcolor{orange}{\textbf{#2}}
    \list{--}{\topsep=2pt\itemsep=0pt\parsep=0pt
              \parskip=0pt\labelwidth=8pt\leftmargin=8pt
              \itemindent=0pt\labelsep=2pt}
    #5
    \endlist
  };
  % New:
  \node [anchor=base west] at (cal-#6.base east) {\textcolor{orange}{\textbf{#2}}};
}  
\end{codeexample}

This is followed by the main mindmap setup\dots

\begin{codeexample}[code only]
\noindent
\begin{tikzpicture}
  \begin{scope}[
    mindmap,
    every node/.style={concept, circular drop shadow,execute at begin node=\hskip0pt},
    root concept/.append style={
      concept color=black,
      fill=white, line width=1ex,
      text=black, font=\large\scshape},
    text=white,
    computational problems/.style={concept color=red,faded/.style={concept color=red!50}},
    computational models/.style={concept color=blue,faded/.style={concept color=blue!50}},
    measuring complexity/.style={concept color=orange,faded/.style={concept color=orange!50}},
    solving problems/.style={concept color=green!50!black,faded/.style={concept color=green!50!black!50}},
    grow cyclic,
    level 1/.append style={level distance=4.5cm,sibling angle=90,font=\scshape},
    level 2/.append style={level distance=3cm,sibling angle=45,font=\scriptsize}]
\end{codeexample}
\dots and contents:
\begin{codeexample}[code only]  
  \node [root concept] (Computational Complexity) {Computational Complexity} % root
      child [computational problems] { node [yshift=-1cm] (Computational Problems) {Computational Problems}
        child         { node (Problem Measures) {Problem Measures} }
        child         { node (Problem Aspects) {Problem Aspects} }
        child [faded] { node (problem Domains) {Problem Domains} }
        child         { node (Key Problems) {Key Problems} }
      }
      child [computational models] { node [yshift=-1cm]  (Computational Models) {Computational Models}
        child         { node (Turing Machines) {Turing Machines} }
        child [faded] { node (Random-Access Machines) {Random-Access Machines} }
        child         { node (Circuits) {Circuits} }
        child [faded] { node (Binary Decision Diagrams) {Binary Decision Diagrams} }
        child         { node (Oracle Machines) {Oracle Machines} }
        child         { node (Programming in Logic) {Programming in Logic} }
      }
      child [measuring complexity] { node [yshift=1cm] (Measuring Complexity) {Measuring Complexity} 
        child         { node (Complexity Measures) {Complexity Measures} }
        child         { node (Classifying Complexity) {Classifying Complexity} }
        child         { node (Comparing Complexity) {Comparing Complexity} }
        child [faded] { node (Describing Complexity) {Describing Complexity} }
      }
      child [solving problems] { node [yshift=1cm] (Solving Problems) {Solving Problems}
        child         { node (Exact Algorithms) {Exact Algorithms} }
        child         { node (Randomization) {Randomization} }
        child         { node (Fixed-Parameter Algorithms) {Fixed-Parameter Algorithms} }
        child         { node (Parallel Computation) {Parallel Computation} }
        child         { node (Partial Solutions) {Partial Solutions} }
        child         { node (Approximation) {Approximation} }
      };
  \end{scope}
\end{codeexample}
Now comes the calendar code:
\begin{codeexample}[code only]
  \tiny
  \calendar [day list downward,
             month text=\%mt\ \%y0,
             month yshift=3.5em,
             name=cal,
             at={(-.5\textwidth-5mm,.5\textheight-1cm)},
             dates=2009-04-01 to 2009-06-last]
    if (weekend)
      [black!25]
    if (day of month=1) {
      \node at (0pt,1.5em) [anchor=base west] {\small\tikzmonthtext};
    };
\end{codeexample}
The lecture annotations:
\begin{codeexample}[code only]
  \lecture{1}{Computational Problems}{above,xshift=-5mm,yshift=5mm}{Computational Problems.north}{
    \item Knowledge of several key problems
    \item Knowledge of problem encondings
    \item Being able to formalize problems
  }{2009-04-08}
    
  \lecture{2}{Computational Models}{above left}
  {Computational Models.west}{
    \item Knowledge of Turing machines
    \item Being able to compare the computational power of different
      models 
  }{2009-04-15}
\end{codeexample}
Finally, the background:
\begin{codeexample}[code only]
  \begin{pgfonlayer}{background}
    \clip[xshift=-1cm] (-.5\textwidth,-.5\textheight) rectangle ++(\textwidth,\textheight);
    
    \colorlet{upperleft}{green!50!black!25}
    \colorlet{upperright}{orange!25}
    \colorlet{lowerleft}{red!25}
    \colorlet{lowerright}{blue!25}

     % The large rectangles:
    \fill [upperleft]  (Computational Complexity) rectangle ++(-20,20);
    \fill [upperright] (Computational Complexity) rectangle ++(20,20);
    \fill [lowerleft]  (Computational Complexity) rectangle ++(-20,-20);
    \fill [lowerright] (Computational Complexity) rectangle ++(20,-20);

    % The shadings:
    \shade [left color=upperleft,right color=upperright]
      ([xshift=-1cm]Computational Complexity) rectangle ++(2,20);
    \shade [left color=lowerleft,right color=lowerright]
      ([xshift=-1cm]Computational Complexity) rectangle ++(2,-20);
    \shade [top color=upperleft,bottom color=lowerleft]
      ([yshift=-1cm]Computational Complexity) rectangle ++(-20,2);
    \shade [top color=upperright,bottom color=lowerright]
      ([yshift=-1cm]Computational Complexity) rectangle ++(20,2);
  \end{pgfonlayer}
\end{tikzpicture}
\end{codeexample}

The next page shows the resulting lecture map in all its glory (it
would be somewhat more glorious, if there were more lecture
annotations, but you should get the idea).

\def\lecture#1#2#3#4#5#6{
  % As before:    
  \node [annotation, #3, scale=0.65, text width=4cm, inner sep=2mm, fill=white] at (#4) {
    Lecture #1: \textcolor{orange}{\textbf{#2}}
    \list{--}{\topsep=2pt\itemsep=0pt\parsep=0pt
              \parskip=0pt\labelwidth=8pt\leftmargin=8pt
              \itemindent=0pt\labelsep=2pt}
    #5
    \endlist
  };
  % New:
  \node [anchor=base west] at (cal-#6.base east) {\textcolor{orange}{\textbf{#2}}};
}

\noindent
\begin{tikzpicture}
  \begin{scope}[
    mindmap,
    every node/.style={concept, circular drop shadow,execute at begin node=\hskip0pt},
    root concept/.append style={
      concept color=black,
      fill=white, line width=1ex,
      text=black, font=\large\scshape},
    text=white,
    computational problems/.style={concept color=red,faded/.style={concept color=red!50}},
    computational models/.style={concept color=blue,faded/.style={concept color=blue!50}},
    measuring complexity/.style={concept color=orange,faded/.style={concept color=orange!50}},
    solving problems/.style={concept color=green!50!black,faded/.style={concept color=green!50!black!50}},
    grow cyclic,
    level 1/.append style={level distance=4.5cm,sibling angle=90,font=\scshape},
    level 2/.append style={level distance=3cm,sibling angle=45,font=\scriptsize}]
    \node [root concept] (Computational Complexity) {Computational Complexity} % root
      child [computational problems] { node [yshift=-1cm] (Computational Problems) {Computational Problems}
        child         { node (Problem Measures) {Problem Measures} }
        child         { node (Problem Aspects) {Problem Aspects} }
        child [faded] { node (problem Domains) {Problem Domains} }
        child         { node (Key Problems) {Key Problems} }
      }
      child [computational models] { node [yshift=-1cm]  (Computational Models) {Computational Models}
        child         { node (Turing Machines) {Turing Machines} }
        child [faded] { node (Random-Access Machines) {Random-Access Machines} }
        child         { node (Circuits) {Circuits} }
        child [faded] { node (Binary Decision Diagrams) {Binary Decision Diagrams} }
        child         { node (Oracle Machines) {Oracle Machines} }
        child         { node (Programming in Logic) {Programming in Logic} }
      }
      child [measuring complexity] { node [yshift=1cm] (Measuring Complexity) {Measuring Complexity} 
        child         { node (Complexity Measures) {Complexity Measures} }
        child         { node (Classifying Complexity) {Classifying Complexity} }
        child         { node (Comparing Complexity) {Comparing Complexity} }
        child [faded] { node (Describing Complexity) {Describing Complexity} }
      }
      child [solving problems] { node [yshift=1cm] (Solving Problems) {Solving Problems}
        child         { node (Exact Algorithms) {Exact Algorithms} }
        child         { node (Randomization) {Randomization} }
        child         { node (Fixed-Parameter Algorithms) {Fixed-Parameter Algorithms} }
        child         { node (Parallel Computation) {Parallel Computation} }
        child         { node (Partial Solutions) {Partial Solutions} }
        child         { node (Approximation) {Approximation} }
      };
  \end{scope}
  
  \tiny
  \calendar [day list downward,
             month text=\%mt\ \%y0,
             month yshift=3.5em,
             name=cal,
             at={(-.5\textwidth-5mm,.5\textheight-1cm)},
             dates=2009-04-01 to 2009-06-last]
    if (weekend)
      [black!25]
    if (day of month=1) {
      \node at (0pt,1.5em) [anchor=base west] {\small\tikzmonthtext};
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  \lecture{1}{Computational Problems}{above,xshift=-5mm,yshift=5mm}{Computational Problems.north}{
    \item Knowledge of several key problems
    \item Knowledge of problem encondings
    \item Being able to formalize problems
  }{2009-04-08}
    
  \lecture{2}{Computational Models}{above left}
  {Computational Models.west}{
    \item Knowledge of Turing machines
    \item Being able to compare the computational power of different
      models 
  }{2009-04-15}
  
  \begin{pgfonlayer}{background}
    \clip[xshift=-1cm] (-.5\textwidth,-.5\textheight) rectangle ++(\textwidth,\textheight);
    
    \colorlet{upperleft}{green!50!black!25}
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     % The large rectangles:
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    \fill [upperright] (Computational Complexity) rectangle ++(20,20);
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    % The shadings:
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