These days do engage in the algorithm-based, network put exile for a few days, and now come to summarize the various variants of network flow, there is a similar topic, then I will try to attach.
Minimum percentage
FIG cutting of so-called, refers to a set of vertices S, issue the set of those edges directed from the outside S S, referred to as cut (S, V \ S). The capacity of these edges are referred to as cut and capacity. Corresponds to FIG stream, if the active point s belong to S ,, the sink t belong to (V \ S), then the time of cutting, also known as s - t cut. If the network s - t cut all the edges are deleted, will no longer have to t s path.
Minimum cut problem: For a given network, in order to ensure that there is no path from s to t, a minimum total capacity of edges to be deleted is how much?
The maximum flow theorem: flow rate equal to the maximum flow capacity of the minimum cut.
Maximum flow variations thereof
1. The plurality of source sink plurality of network flows:
Establishing super source point s, and the establishment of the point source from the super capacity to other source is infinite, the establishment of super sink, built from the meeting point to the other point of a super capacity is infinite sink side. The maximum flow can be determined from s to t.
2. No maximum flow onto the graph:
The transition to non-view of a directed graph need only undirected graph capacity c establishing a reverse side edges, two edges exist, the maximum flow can be determined.
3. there is a case of capacity limitations on the vertices:
Drawing not only on the edge has a limited capacity, but also the way through the apex of the inflow What about two out of the total amount limit should deal with it? After this time we get two vertices each vertex can be split into two vertices are split into vertex point and the vertex, will point to the original vertex point edge into the apex, apex pointed edges from the original change from the apex pointed out. And then connected to the apex of the capacity from the original edge vertices to vertices capacity, capacity constraints can be put into the apex of the edge capacity constraints.
4. There is minimal flow restrictions:
Refers not only each side stream C has a maximum limit, and where B is the minimum flow limit, i.e., (B (e) <= f (e) <= C (e)). So that f '(e) = f (e) - B (e), which can be converted into a case where only the maximum flow limit, i.e., 0 <= f' (e) <= C (e) - B (e) .
At this time, the relationship between the vertices corresponding to the total inflow and outflow amount is changed
Dig a hole, after his game fix on, and now to do the template title, trained, trained, trained,