Push-Relabel算法

Ford-Fulkerson方法还比较好理解

即每一次尝试都需要在剩余图里找到一条增强路径。让整个图的流量最大化。

Algorithm Operation(s)	Residual Graph
Initialize the residual graph by setting the preflow to values 0 and initializing the labeling.
Initial saturating push is performed across all preflow edges out of the source, s.
Vertex a is relabeled in order to push its excess flow towards the sink, t. The excess at a is then pushed to b then d in two subsequent saturating pushes; which still leaves a with some excess.
Once again, a is relabeled in order to push its excess along its last remaining positive residual (i.e. push the excess back to s). The vertex a is then removed from the set of active vertices.
Relabel b then push its excess to t and c.
Relabel c then push its excess to d.
Relabel d then push its excess to t.
This leaves the vertex b as the only remaining active vertex, but it cannot push its excess flow towards the sink. Relabel b then push its excess towards the source, s, via the vertex a.
Push the last bit of excess at a back to the source, s. There are no remaining active vertices. The algorithm terminates and returns the maximum flow of the graph (as seen above).

理解了好久。记录一下。
这个算法主要的要点是这些：

1、尽可能多的（在边容纳范围内）向sink方向增大流。

2、source和sink的height都是定死的，一个是|V|另一个是0

3、height可以理解成该站的水位。如果比周围的站点都高，那他们就不能向此处增大流。

4、指针的意思是，A到B站可以还可以增大N个单位的流

5、流的唯一出口是sink节点。程序收敛时，每一个站要么已经没有库存流，要么无法向高位置的站发送流。（位高是由于边流量限制引发）