# Further Maths - Route Inspection

> Source: https://ollybritton.com/notes/a-level/further-maths/topics/route-inspection/ · Updated: 2021-11-17 · Tags: school

## Flashcards
##### How could you summarise the route inspection problem??
Find a route of minimum weight that traverses every edge at least once, starting and ending at the same vertex.

##### Why will a Eulerian trail solve the route inspection problem minimally??
Because it traverses every edge exactly once, so it keeps edge weights to a minimum.

##### When there are two odd verticies and you're trying to solve a route inspection problem, what should you do??
Find the shortest route between them and double those edges.

##### When there are more than two odd vertices in a graph, what should you do before performing the route inspection algorithm??
Consider all the ways they could pair up and pick the two that increase the weight by the smallest amount.

##### How can you quickly calculate the total cost of the minimum Eulerian trail after doubling up a few verticies??
Add up all the weights and then the weight of the shortest path between the odd vertices.

##### For route inspection with 4 odd vertices and starting and ending in different places, after tabulating all possible pairings you have a list of path costs between them. Which pair should you choose to double up rather than start and end there??
The pair with the smallest cost should be doubled.

### 2022-03-17
##### When doubling up vertices for route inspection, what do you have to consider apart from direct connections??
Whether there is any route going through multiple vertices that's shorter.

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