Edmonds Flowering algorithm

Edmonds Flowering algorithm

Input

Figure g, matched M, not saturation point u

Idea

find m-interleaved paths starting from U. record father node for each vertex 。

Discover the flowers. is shrunk.

Dimension protect S and T. S represents the set of vertices that are reached along an already saturated edge. The new vertex in the contraction process also belongs to S.

T represents the set of vertices that are reached in the current diagram along an unsaturated edge, and once an unsaturated vertex is encountered. The augmented path is obtained.

Init:

S = {u}, T =?

Iterate:

If there are no unsaturated points in S, there is no augmented path from the U start. The algorithm stops.

Otherwise, take out an unsaturated vertex v∈s and consider y in turn? The random vertex of T y∈n (v).

If Y is not saturated with M, the trace starts from Y. If necessary, the flowering, output augmentation path.

If Y∈s. Then find the flowers. Shrink the flowers and replace the corresponding vertices in S and T with the new vertices that are produced.

Start the search from a new point such as the resulting new diagram.

Otherwise. Y is matched by M to a vertex w. The Y record is reached by V and placed in T, and W is marked by Y and placed in S.

After processing all of the V neighbors, Mark V. Continue the iteration.

Edmonds Flowering algorithm