Version 5.0 The LEDA User Manual

in general graph.
You may skip the following subsections and restrict on reading the function signatures
and the corresponding comments in order to use these functions. If you are interested in
technical details, or if you would like to ensure that the input data is well chosen, or if
you would like to know the exact meaning of all output parameters, you should continue
reading.
The functions in this section are template functions. It is intended that in the near
future the template parameter NT can be instantiated with any number type. Please
note that for the time being the template functions are only guaranteed to
perform correctly for the number type int. In order to use the template version of
the function the appropriate .h-file must be included.
#include
There are pre-instantiations for the number types int. In order to use them either
#include
or
#include
has to be included (the latter file includes the former). The connection between template
functions and pre-instantiated functions is discussed in detail in the section “Templates
for Network Algorithms” of the LEDA book. The function names of the pre-instantiated
versions and the template versions only differ by an additional suffix _T in the names of
the latter ones.
Proof of Optimality. Most of the functions for computing maximum or minimum
weighted matchings provide a proof of optimality in the form of a dual solution represented
by pot, BT and b. We briefly discuss their semantics: Each node is associated with a
potential which is stored in the node array pot. The array BT (type array) is used to represent the nested family of odd cardinality sets which is constructed
during the course of the algorithm. For each (non-trivial) blossom B, a two tuple (z B , p B )
is stored in BT, where z B is the potential and p B is the parent index of B. The parent
index p B is set to −1 if B is a surface blossom. Otherwise, p B stores the index of the
entry in BT corresponding to the immediate super-blossom of B. The index range of
BT is [0, . . . , k − 1], where k denotes the number of (non-trivial) blossoms. Let B ′ be a
sub-blossom of B and let the corresponding index of B ′ and B in BT be denoted by i ′
and i, respectively. Then, i ′ < i. In b (type node array) the parent index for each
node u is stored (−1 if u is not contained in any blossom).