Version 5.0 The LEDA User Manual

12.10 Stable Matching ( stable matching )
We are given a bipartite graph G = (A∪B, E) in which the edges incident to every vertex
are linearly ordered. The order expresses preferences. A matching M in G is stable if
there is no pair (a, b) ∈ E \ M such that (1) a is unmatched or prefers b over its partner
in M and (2) b is unmatched or prefers a over its partner in M. In such a situation a
has the intention to switch to b and b has the intention to switch to a, i.e., the pairing is
unstable.
We provide a function to compute a correct input graph from the preference data, a
function that computes the stable matching when the graph is given and a function that
checks whether a given matching is stable.
void StableMatching(const graph& G, const list& A,
const list& B, list& M)
The function takes a bipartite graph G with sides A
and B and computes a maximal stable matching M
which is A-optimal. The graph is assumed to be bidirected,
i.e, for each (a, b) ∈ E we also have (b, a) ∈ E.
It is assumed that adjacency lists record the preferences
of the vertices. The running time is O(n + m).
Precondition: The graph G is bidirected and a map.
Sets A and B only contain nodes of graph G. In addition
they are disjoint from each other.
bool CheckStableMatching(const graph& G, const list& A,
const list& B, const list& M)
returns true if M is a stable matching in G. The
running time is O(n + m).
Precondition: A and B only contain nodes from G.
The graph G is bipartite with respect to lists A and
B.