Version 5.0 The LEDA User Manual

The pre-instantiations for number type double compute the optimal matching for a modified
weight function c1 , where for every edge e
c1 [e] = sign(c[e])⌊|c[e]| · S⌋/S
and S is the largest power of two such that S < 2 53 /(f · C).
The weight of the optimal matching for the modified weight function and the weight of
the optimal matching for the original weight function differ by at most n · f · C · 2 −52 .
template
list MAX WEIGHT BIPARTITE MATCHING T(graph& G,
const edge array& c,
node array& pot)
computes a matching of maximal cost and a potential function pot that
is tight with respect to M. The running time of the algorithm is O(n ·
(m + n log n)). The argument pot is optional.
Precondition: G must be bipartite.
template
list MAX WEIGHT BIPARTITE MATCHING T(graph& G,
const list& A,
const list& B,
const edge array& c,
node array& pot)
As above. It is assumed that the partition (A, B) witnesses that G is
bipartite and that all edges of G are directed from A to B. If A and
B have different sizes then is is advisable that A is the smaller set; in
general, this leads to smaller running time. The argument pot is optional.
template
bool CHECK MWBM T(const graph& G, const edge array& c,
const list& M, const node array& pot)
checks that pot is a tight feasible potential function with respect to M
and that M is a matching. Tightness of pot implies that M is a maximum
weighted matching.
template
list MAX WEIGHT ASSIGNMENT T(graph& G, const edge array& c,
node array& pot)
computes a perfect matching of maximal cost and a potential function
pot that is tight with respect to M. The running time of the algorithm
is O(n · (m + n log n)). If G contains no perfect matching the empty set
of edges is returned. The argument pot is optional.
Precondition: G must be bipartite.