\chapter{Introduction} \label{Introduction}
\pagenumbering{arabic}

One of the major differences between combinatorial computing
and other areas of computing such as statistics, numerical
analysis and linear programming is the use of complex data types. 
Whilst the built-in types, such as integers, reals, vectors, and matrices,
usually suffice in the other areas, combinatorial computing relies heavily 
on types like stacks, queues, dictionaries, sequences, sorted sequences, 
priority queues, graphs, points, segments, $\ldots$
In the fall of 1988, we started a project (called {\bf LEDA} for Library of
Efficient Data types and Algorithms) to build a small, but growing library 
of data types and algorithms in a form which allows them to be used by 
non-experts. We hope that the system will narrow the gap between algorithms
research, teaching, and implementation. The main features of LEDA are:

\begin{enumerate}
\item 
    LEDA provides a sizable collection of data types and algorithms in a form 
    which allows them to be used by non-experts. In the current version, this
    collection includes most of the data types and algorithms described in the 
    text books of the area. 

\item 
    LEDA gives a precise and readable specification for each of the data types 
    and algorithms mentioned above.  The specifications are short (typically, 
    not more than a page), general (so as to allow several implementations), 
    and abstract (so as to hide all details of the implementation). 

\item
    For many efficient data structures access by position is important. In 
    LEDA, we use an item concept to cast positions into an abstract form. We 
    mention that most of the specifications given in the LEDA manual use this 
    concept, i.e., the concept is adequate for the description of many data 
    types. 

\item
    LEDA contains efficient implementations for each of the data types, e.g., 
    Fibonacci heaps for priority queues, skip lists and dynamic perfect 
    hashing for dictionaries, ...


\item
    LEDA contains a comfortable data type graph. It offers the standard 
    iterations such as ``for all nodes v of a graph G do'' or ``for all 
    neighbors w of v do'', it allows to add and delete vertices and edges 
    and it offers arrays and matrices indexed by nodes and edges,...  
    The data type graph allows to write programs for graph problems in a 
    form close to the typical text book presentation.


\item 
    LEDA is implemented by a \CC class library. It can be used with almost
    any \CC compiler (e.g., cfront, \gg (versions $>=$ 2.5), sunpro, watcom, 
    emx, bcc, ztc).


\item
    {LEDA is available by anonymous ftp from {\bf ftp.mpi-sb.mpg.de} in
    directory /pub/LEDA. The distribution contains all sources, installation 
    instructions, a technical report, and the user manual.}


\item
    LEDA is not in the public domain, but can be used freely for research 
    and teaching. Information on a commercial license is available from the 
    author or leda@mpi-sb.mpg.de.

\end{enumerate}

This manual contains the specifications of all data types and algorithms 
currently available in LEDA. Users should be familiar with the \CC 
programming language (see \cite{S91} or \cite{Li89}).  The manual 
is structured as follows: In chapter one, which is a prerequisite for all
other chapters, we discuss the basic concepts and notations used in LEDA.
The other chapters define the data types and algorithms available in
LEDA and give examples of their use. These chapters can be consulted
independently from one another.

\bigskip
\bigskip
{\large\bf Version 3.0}

The most important changes with respect to previous versions are

\begin{enumerate}
\item 
Parameterized data types are realized by \CC templates. In particular, 
{\it declare} macros used in previous versions are now obsolete and the 
syntax for a parameterized data type $D$ with type parameters $T_1,\dots,T_k$ 
is $D\<T_1,\dots,T_k\>$ (cf. section \ref{Specifications}). For \CC compilers not
supporting templates there is still a non-template variant (LEDA-N-3.0) 
available.

\item
Arbitrary data types (not only pointer and simple types) can be used as
actual type parameters (cf. section \ref{Specifications}). 

\item
For many of the parameterized data types (in the current version: dictionary, 
priority queue, d\_array, and sortseq) there exist variants taking an additional
data structure parameter for choosing a particular implementation 
(cf. section \ref{Implementation Parameters}).

\item
The LEDA memory management system can be customized for user-defined classes
(cf. section \ref{Memory Management})

\item
The efficiency of many data types and algorithms has been improved.
\end{enumerate}

See also the ``Changes" file in the LEDA root directory.


\newpage
{\large\bf Version 3.1}

Many changes were made to make LEDA work with new compilers (\gg-2.6.3,
Lucid \CC, Watcom \CC Sunpro \CC, ...) and on more platforms (Silicon 
Graphics, IBM, HP, Solaris-2.3, Linux, ...). All reported bugs of version
3.0 we were able to find and understand have been fixed (see LEDA/Fixes
for a list). Several new data types and algorithms (especially in the graph 
and window section) have been included.



\bigskip
{\bf Manual Pages}

  All manual pages have been incorporated into the corresponding
  header files. There are tools (LEDA/util/manual) to extract and
  typeset the new user manual from these files. A postscript and
  LaTeX version of the manual is available on the ftp server.


\bigskip
{\bf Parameterized Data Types}

  The  LEDA\_TYPE\_PARAMETER macro that had to be called for type
  arguments in parameterized data types when using the \gg compiler
  is not needed anymore for \gg versions $>=$ 2.6.3.


\bigskip
{\bf Linear Orders, I/O, and Hashing}

  $compare$, $Hash$, $Read$ and $Print$ functions only have to be 
  defined for type parameters of a parameterized data type if they are 
  actually used by operations of the data type. If one of these function 
  is called and has not been defined explicitely, a default version giving
  an error message is instantiated from a function template.
  Except for the built-in types and some basic LEDA types ($string$ and
  $point$) there are no predefined versions of these functions any more.
  In particular, they are not predefined for arbitrary pointer types. 
  You will notice the effect of this change, for instance, when calling 
  the sort operation on a list of pointers $list\<T*\>$ without a definition 
  of a compare function for $T*$.  Previous LEDA 
  releases sorted the list by increasing addresses of the pointers in 
  this case. In version~3.1 the program will exit with the exception
  ``no compare function defined for $T*$". Operations based on functions
  $Hash$, $Read$, or $Print$ show a similar behavior.

\bigskip
{\bf Nested Forall Loops }

   The limitation of previous versions that {\bf forall}-loops (e.g.
   on lists) could not be nested is no longer valid.



\bigskip
{\bf Graphs}

The distinction in directed and undirected graphs is not as strict as
in previous versions. Data type $graph$ represents both directed and
undirected graphs. Directed and undirected graphs only differ in the
definition of adjacent edges or nodes. Now, two lists of edges are 
associated with every node $v$: the list
$out\_edges(v) = \{\ e \in E\ | source(e) = v\ \}$ of edges starting in $v$,
and the list $in\_edges(v) = \{\ e \in E\ | target(e) = v\ \}$ of
edges ending in $v$. 
A graph is either {\em directed} or {\em undirected}.
In a directed graph an edge is adjacent to its source and in an undirected
graph it is adjacent to its source and target. In a directed graph a node $w$
is adjacent to a node $v$ if there is an edge $(v,w) \in E$; in an undirected
graph $w$ is adjacent to $v$ if there is an edge $(v,w)$ or $(w,v)$ in the
graph.  There are iteration macros allowing to iterate over the list of
starting, ending or adjacent edges (cf. \ref{Graphs} for details).


\bigskip
{\bf New Data Types}

The old priority queue type $priority\_queue\<K,I\>$ caused
a lot of confusion because of the non-standard semantics of the type 
parameters $K$ and $I$ (the meaning of {\em key} and {\em information} 
was exchanged compared to most text book presentations of priority queues).
To eliminate this confusion we introduced a new priority queue type
$p\_queue\<P,I\>$. Now $P$ is called the priority type of the queue.

The basic library has been extended by several numerical data types
including an arbitrary length integer type ($integer$), a type of
rational numbers ($rational$), and two filter types $floatf$ and
$real$. Together with the new types $rat\_point$ (points with rational 
coordinates) and $rat\_segments$ (segments with rational coordinates) 
they are especially useful in geometric computations. Note, that the
geometric part of LEDA will be extended by more basic objects and
algorithms based on exact arithmetic in the near future.

The temporarily (in LEDA-3.1c) introduced data types $node\_data$,
$node\_stack$, $node\_queue$ are no longer available. Please use $node\_map$, 
$edge\_map$, $stack\<node\>$ and $queue\<node\>$ instead.

A list of the new data types:\\
\begin{itemize}
\item
priority queues     ($p\_queue<P,I\>$) (cf. \ref{Priority Queues})
\item
singly linked lists ($slist\<T\>$)     (cf. \ref{Singly Linked Lists})
\item
big integers        ($integer$)        (cf. \ref{Integers of Arbitrary Length})
\item
rational numbers    ($rational$)       (cf. \ref{Rational Numbers})
\item
rational points     ($rat\_point$)     (cf. \ref{Rational Numbers})
\item
rational segments   ($rat\_segment$)   (cf. \ref{Rational Numbers})
\item
floating point filter ($floatf$)       (cf. \ref{A Floating Point Filter})
\item
random sources      ($random\_source$) (cf. \ref{Random Sources})
\item
real numbers        ($real$)           (cf. \ref{Real Numbers})
\item
maps                ($map\<I,E\>$)     (cf. \ref{Maps})
\item
node  maps          ($node\_map\<T\>$) (cf. \ref{Node Maps})
\item
edge maps           ($edge\_map\<T\>$) (cf. \ref{Edge Maps})
\item
node lists          ($node\_list$)     (cf. \ref{Lists of Nodes})
\item
bounded node priority queues $b\_node\_pq\<n\>$ (cf. \ref{Bounded Node Priority Queues}).

\end{itemize}


\bigskip
{\bf Graph Generators and Algorithms}

LEDA now offers more generators for different types of graphs (see 
\ref{Graph Generators} for a complete list).
The planarity test $PLANAR$ has been re-implemented and
now has a boolean flag parameter $embed$. An embedding of the graph
is computed only if $embed = true$. A second variant of $PLANAR$
computes a Kuratowsky-subgraph in the case of non-planarity.
A new graph algorithm is $MIN\_COST\_MAX\_FLOW$ computing
a maximal flow with minimal cost. 


\bigskip
{\bf Windows and Panels}

The window and panel data types  now are based on a plain X11 implementation.
New features include\\
-- opening more than one window or panel\\
-- positioning, displaying, and closing of panels and windows\\
-- changing the label of windows and panels\\
-- 16 predefined colors\\
-- accessing colors from the X11 data base by name\\
-- drawing arcs, arc edges, and arc arrows\\
-- changing the default fonts, \\
-- reading and handling X11 events\\
-- a simple graph editor (cf. \<LEDA/graph\_edit.h\>)\\

