Version 5.0 The LEDA User Manual

template
bool CHECK MIN WEIGHT ASSIGNMENT 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 perfect matching. Tightness of pot implies that M is a
minimum cost assignment.
template
list MWMCB MATCHING T(graph& G, const list& A,
const list& B, const edge array& c,
node array& pot)
Returns a maximum weight matching among the matching of maximum
cardinality. The potential function pot is tight with respect to a modified
cost function which increases the cost of every edge by L = 1+2kC where
C is the maximum absolute value of any weight and k = min(|A|, |B|).
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, it is advisable that A is the smaller set; in general, this leads to
smaller running time. The argument pot is optional.
bool MWBM SCALE WEIGHTS(const graph& G, edge array& c)
replaces c[e] by c1 [e] for every edge e, where c1 [e] was defined above
and f = 3. This scaling function is appropriate for the maximum weight
matching algorithm. The function returns false if the scaling changed
some weight, and returns true otherwise.
bool MWA SCALE WEIGHTS(const graph& G, edge array& c)
replaces c[e] by c1 [e] for every edge e, where c1 [e] was defined above
and f = 4n. This scaling function should be used for the algorithm
that compute minimum of maximum weight assignments or maximum
weighted matchings of maximum cardinality. The function returns false
if the scaling changed some weight, and returns true otherwise.
12.8 Maximum Cardinality Matchings in General
Graphs ( mc matching )
A matching in a graph G is a subset M of the edges of G such that no two share an
endpoint.
An odd-set cover OSC of G is a labeling of the nodes of G with non-negative integers
such that every edge of G (which is not a self-loop) is either incident to a node labeled 1