Graph Theory (updating ing)

Largest group

Problem description: A group is the largest complete subgraph.

Given undirected graph G = (V, E ). If UV, and for any U, VU has (u, v) e, it is called u
Is the complete subgraph of G.

The complete subgraph U of G is a group of G, and only when u is not included in a larger complete subgraph of G, that is, U is the largest complete subgraph.

The largest group of G refers to the group with the largest number of vertices in G.

For example:

(A) (B) (c) (d)

Figure A is an undirected graph. Figures B, C, and D are the largest and the largest groups in Figure.

The things of the largest group:

First, set the largest group to an empty group, add a vertex to it, and then consider each vertex in sequence. After the vertex is added to the group, it still forms a group. If yes, consider adding the vertex to a group or dropping it. If not, discard it directly and then determine the next vertex recursively. In the case of no connection or directly discard, the pruning policy can be used before recursion to avoid invalid search.

To determine whether the current vertex is still a consortium after joining the consortium, you only need to consider whether the vertex and the consortium vertices are connected.

The program adopts a simple pruning strategy, that is, if the remaining number of unconsidered vertices plus the number of top points in the group is not greater than the number of vertices of the current solution, you can stop the deep search, otherwise, continue with deep recursion.

When a leaf knot is found, the search can be stopped. At this time, the optimal and Optimal Values are updated.

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Minimum Cut

Cut: Set CI to a set of several arcs in network N. If all the arcs in the CI are deleted from N, that is, when the path set from vertex vs to vertex VT is empty, it is called a cut between Vs and vt.

Minimum Cut: if any arc is deleted from the CI, the CI will no longer be the cut between Vs and VT, and the cut will satisfy the minimum cut or be the minimum cut.

Http://baike.baidu.com/view/10778678.htm)

Cut is the Flow Network G = (V, E) cut (S, T) will be divided into S and T = V-S two parts, making S, T
That is, the origin and sink are in two different subsets.
The minimum cut refers to the smallest cut in the stream network capacity.

Min cut = max stream !!!

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Minimum vertex overwrite or least vertex Overwrite

In a bipartite graph, find the least vertex so that these vertices can overwrite all edges.

Minimum vertex overwrite = maximum match !!!

Minimum Point Weight Overwrite

In a bipartite graph (divided into parts X and parts y), select some vertices to overwrite all edges, and the selected vertex weight value is the smallest (here the vertex has the right value !!!)

Model Creation:

Create Source Vertex S and sink vertex T. In the original Binary Graph, if edge u -- V exists, create the vertex weight of edge s -- U, and u -- V is INF, vertices with the V -- t weight as V

Minimum Point Weight overwrite = Minimum Cut = maximum stream !!!

Maximum vertex weight coverage

Maximum vertex weight overwrite = sum-minimum vertex weight overwrite !!!

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