A summary of network flow modeling

There are many major competitions in the network flow modeling problems, and for like me (=) such as Konjac Konjac is a solution, or "old question casually a, the new question will never" attitude, so open this post to summarize some of the model of network flow modeling bar, constantly updated.

1. Allocation problem : As the name implies, a collection is decomposed into a number of small sets of topics.

common cliché:"Now we have a batch of goods to be transported to a place by some road ... "," Each game can provide two points for the total score, either one point per team (draw), or 2-0 (one team wins) ... "," a piece of cake, and now there are N cooks coming, each one can cut several ... "The essence of these problems is the distribution problem.

Typical examples: COJ0503

The idea of solving problems : In fact, the arcs we draw include the principle of our distribution, for the distribution of reasonable arcs, we may wish to consider from the following points:

1. Allocation of the upper limit: For each game we can allocate two points, for each game we think of as a point, then the reasonable distribution plan only two points will not be more than a few, then for each game, we just give the flow at the beginning of the time only to 2 traffic will guarantee its upper limit , the lower limit can be resolved by other means. This method of limiting the amount of traffic (capacity) in the source point to a certain unit can be called a "control source"and the control source can help us determine the upper limit of the allocation.

2. Assigned objects: or example: For each game we can only assign points to the two teams, then we only need to treat each team as a point, the game allocation points can be abstracted as a race node to two team nodes to allocate these 2 traffic, we have to do is to ensure that traffic can pass them on the line, So we built a non-capacity-capped connection game and two teams of arcs to complete the flow of traffic. This method of solving the distribution problem by means of an arc with no capacity limit to ensure the flow connection so that we can call it "drainage", drainage can help us determine the assigned object.

Note: The key word of drainage is "concise, clear", a very good drainage in complex modeling is very important, the blind lead will completely destroy the design intention.

If we find mutual influence in the drainage, we must take a decisive break, can see POJ 2391.

2. Limitations : As the name implies, the problem of solving a constrained system.

common cliché:"Now can we meet the rationality of these distributions ... "

Problem- Solving ideas: The limitation is often the treatment of other problems, often with the dichotomy method, counting method and so on. We can start with a discussion on "The rationality of distribution issues":

Full-Stream allocation: full-flow allocation refers to the amount of traffic calculated is equal to the total allocation, usually if this ensures the legitimacy of the full distribution, of course, specific problems to be analyzed.

We estimate that the allocation number can be recorded as "standard", the actual maximum flow can be recorded as "real Flow", then meet the full stream allocation when and only if the standard amount = real traffic.

3. Dynamic flow problem : It is a little bit of adding edge to the original image.

Common cliché: a variety of times, you can stay like this ...

Typical examples: SGU0483

The idea of solving problems: It is usually to enumerate the time, construct a layered network , and then become a constraint problem.

Network flow or a lot of a problem to have experience it, constantly updated.

Reprint please indicate the source http://www.cnblogs.com/chxer/, thank you! Chxer

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A summary of network flow modeling