Version 5.0 The LEDA User Manual

Chapter 12
Graph Algorithms
This chapter gives a summary of the graph algorithms contained in LEDA, basic graph
algorithms for reachability problems, shortest path algorithms, matching algorithms, flow
algorithms, . . . .
All graph algorithms are generic, i.e., they accept instances of any user defined parameterized
graph type GRAP H as arguments.
All graph algorithms are available by including the header file
. Alternatively, one may include a more specific header file.
An important subclass of graph algorithms are network algorithms. The input to most
network algorithms is a graph whose edges or nodes are labeled with numbers, e.g.,
shortest path algorithms get edge costs, network flow algorithms get edge capacities,
and min cost flow algorithms get edge capacities and edge costs. We use NT to denote
the number type used for the edge and node labels.
Most network algorithms come in three kinds: A templated version in which NT is a
template parameter, and reinstantiated and precompiled versions for the number types
int (always) and double (except for a small number of functions). The function name of the
templated version ends in T. Thus MAX FLOW T is the name of the templated version
of the max flow algorithm and MAX FLOW is the name of the instantiated version.
In order to use the templated version a file must be
included, e.g., in order to use the templated version of the maxflow algorithm, one must
include
Special care should be taken when using network algorithms with a number type NT
that can incur rounding error, e.g., the type double. The functions perform correctly if
the arithmetic is exact. This is the case if all numerical values in the input are integers
(albeit stored as a number of type NT ), if none of the intermediate results exceeds the
maximal integer representable by the number type (2 52 in the case of doubles), and if no
round-off errors occur during the computation. We give more specific information on the
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