Understanding Reduction Hierarchies

Question

I am very interested in understanding how the hierarchy reduction algorithm works. I found this page: https://www.mjt.me.uk/posts/contraction-hierarchies/ and read a lot of new things. I understood how the algorithm works and works, except for one part. I did not understand how the reduction strategy really works. (Important: I do not know math).

In the first example on the page above, the compression order is 6 → 8 → 3 → 0 → 5 → 7 → 4 → 1 → 2 → 9, and I can't understand why. The explanations are not clear to me, and the original article contains too much mathematics.

Can someone explain the strategy used to determine the reduction order? Thank.

Answer 1

It is unclear how they chose the order for their example. Each order leads to the correct algorithm, so it does not really matter. Orders that prevent deep nesting and orders that allow you to add many quick access edges increase efficiency, as is observed both in the article and in the original article.