Edmonds Flowering algorithm

Edmonds Flowering algorithm

Input

Figure g, matched M, not saturation point u

Idea

Find M-interleaved paths starting from U, records the Father node for each vertex. when a flower is found, it shrinks.

Dimension The guard S and T,s represent the set of vertices that are reached along the saturated edges, and the new vertices in the shrinking process belong to S,

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

Init:

S = {u}, T =?

Iterate:

If there is no unsaturated point in S, there is no augmented path starting from U, and the algorithm stops.

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

If Y is not saturated with M, the trace starts from Y and, if necessary, blooms and outputs the augmented path.

If y∈s, the flowers are found, the flowers are shrunk, and the corresponding vertices in S and T are substituted with the new vertices that are produced.

Start searching from this new point of 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 all the neighboring points of V have been processed, Mark V to continue the iteration.

Edmonds Flowering algorithm