Network Flow Summary

Network streams mainly include:

1. Maximum stream

2. Billing Flow

3. Network streams with Upper and Lower Bounds

Basic network stream skills:

1. Multiple Source and Sink points. Create a super source point and a super sink point.

2. There is a capacity limit on the vertex. Split it into two points. The two points are connected to the edge, and the capacity is the capacity limited by the original point.

3. the maximum fee is converted to the minimum fee. Change to negative.

1. Maximum stream

The idea of the largest stream algorithm is to constantly find the path from S to T. The algorithm efficiency is determined by the method for finding the augmented path.

Edmond-Karp Algorithm: Search for augmented path with wide search, time complexity O (N * m ). The simplest way of thinking.

SAP algorithm: The allowable arc is used to search for the augmented path and the dinic algorithm is used for optimization. The time complexity is O (M * n ).

Dinic algorithm: the time complexity is O (M * n ).

Personal experience: Generally, you do not need to modify the algorithm (Template) for the question of the largest stream. The difficulty lies in how to convert the problem into the biggest stream. Creating a graph is a difficult problem. Clever graph creation can reduce the number of points, thus reducing the time complexity. There is a document called network stream modeling summary, which is very well done.

Question link http://www.cnblogs.com/Potato-lover/category/611621.html

1. Determine full stream

3572 task schedule

2883 kebab

2. Binary + maximum stream

Portal:

3. Maximum short circuit + maximum flow

3416 marriage match IV

Ii. Billing Flow

In general, the minimum fee is calculated under the maximum flow condition.

Algorithm: continuous shortest path.

Time complexity O (C * K * m), C is the final traffic, and K * m is the time complexity of the spfa algorithm.

Link: http://www.cnblogs.com/Potato-lover/category/615756.html

3. Network streams with Upper and Lower Bounds

Summary: http://www.cnblogs.com/Potato-lover/p/4002823.html

Network Flow Summary