A summary of the problems of binary graph & network Flow & Minimum Cut

The basis of the binary chart:

Maximum match: Hungarian algorithm

Minimum point overwrite = maximum match

Minimum edge overlay = Total number of nodes-Maximum match

Maximum independent set = points-Maximum match

Network flow:

Bounded network Stream

Summary of minimum cut issues:

* Meaning

1. The edge of the INF is not cut, and is usually used to indicate that a point must belong to a collection

The Edge (S,U,W) represents a cost if u does not cut in S. W

2. The Edge (U,V,W) represents if you cut in S, v in T cut need to pay a price w but note that if u cut in T, V in S cut is not to pay the price. So if the edge (U,v,w) and (V,U,W) indicate that you have to pay a price when you are different from V-owned cut W

* Tips

0. When you ask for the biggest problem, you often use sum minus the cost

This cost is minimal and can be solved with minimal cuts

1. Two points i,j belong to a different set when the Val price is paid

New Point K (S,k,val) (K,i,inf) (K,j,inf)

When Vals,valt is different, you usually create a new point

But at the same time, it is possible to direct (U,V,W) (v,u,w) to pay the W price in the absence of a set

Example: bzoj1497,bzoj2127,bzoj1934

2. Two points belong to the same set pay Val price

At this time, the nature of the graph is a binary graph. (Face-beating

Then we can flip the nature of the two-part point, that is, the left point is selected, and the right point even T is selected.

So after the transformation the problem became the first one. And just (I,j,val) (J,i,val)

Example: bzoj1976,bzoj2132,bzoj3275

Difficult topics:

SRM558 Div1 C

Solution:

A point is split into x1,x2, which indicates whether they have stones or not, and whether there are stones around them.

X1 Yield v-c,x2 yield V, add up the possible gains, minus the minimum cost

If both are selected, pay the price of V

If the adjacent lattice x, y x2 satisfied and Y1 not satisfied, pay the cost inf

A summary of the problems of binary graph & network Flow & Minimum Cut