Summary of basic knowledge points of operations research (8)

A full set of operations research knowledge points

Chapter 8 Graph Theory Methods

1. The basic concept of graphs

1. Basic elements of graphs: nodes, edges
2. Directed graph: all edges have directions
3. Undirected graph: all edges have no direction
4. Connected graph: all nodes are connected and there is no isolated point graph
5. Disconnected graphs: graphs with isolated nodes
6. Power: Information assigned to a node or edge
7. Loop (circle): starting from a point, but also a way back to the origin

Second, the tree and the gradual generation method of the tree

1. Tree: A graph that is connected and does not contain cycles (loops) is called a tree
2. The number of edges of the tree = the number of nodes -1

Three, the smallest branch tree concept

The problem of the smallest branch tree is about finding one or several routes from a starting point to all points in a network so that the total length of all branches used in such routes is the smallest.

Fourth, the concept of the smallest branch tree

Cruz Carr Method (Avoiding Circle Method)

1. Choose the smallest length among the remaining sides each time.
2. The later-selected edge and the already-selected edge cannot form a loop, if they do, they will be discarded
3. Repeat 1 and 2 to know that all edges are selected. It is
   only suitable for smaller networks.
   Prime method: more widely used.
   Calculate from the starting point, the smallest distance

Five, the shortest route problem

The shortest route problem is the problem of finding the route with the least distance or cost between two points when the time, distance, or cost required to pass through each side of the network is known.
The method of the shortest path problem is the reverse algorithm

Sixth, the maximum flow problem

When objects, capabilities, or information are used as traffic to pass through the network, how to maximize the amount of network traffic that flows through, or minimize the cost or time of the network traffic that flows through, the
maximum traffic problem is that under certain conditions, it is required to flow through the network. Flow is the biggest problem

Seven, the application of three solving methods in practice

1. The problem of the smallest branch tree is mainly used in the laying of channels, telephone lines, wires, network cables, etc. (the total route is the shortest)
2. The short-circuit problem is when the time, distance or cost required to pass through each side of the network is known, the problem of finding the route with the shortest distance or the least cost between two points (the shortest distance between two points)
3. The maximum flow problem is the problem that requires the flow of the network to be the largest under certain conditions.