Principle of Internet IP-based global routing optimization-dijkstra algorithm proof

The weekend continues to write half of what was filled, in order to achieve the perfect day.
We know a fact that there are too many IP addresses. Unified management is not possible, whether from the control plane from the data/management layer, the aircraft is so.

So. The IP protocol is designed to be scalable. For IP routing terminology, hop routing is calculated. Of course, support "source routing", source routing means that the data before the departure of the route has been planned, hop-on routing is the standard form of IP routing. Other words. IP packets are planned on the road in real time.
I prefer IP routing because it's also the way I travel, I like to travel, but I don't like to book hotels beforehand. Plan your route in advance. Navigation and so on, my way is to see the road signs on the way forward. To the temporary stop in the place after the backpack to find a place to live, and then go to where to calculate, this is a walk on the walk and no destination wandering ... Of course, IP packets are destined.
Hop-through global optimization IP routing is per-hop routing on each router. Then a problem arises. A huge internet, how to believe that so many hop-on route stitching up a complete path is really the most optimized? The answer is clearly definite. The question is how to prove it.

Routing algorithms in the book, the routing algorithm is basically divided into the distance vector algorithm and link state algorithm, the respective protocol masterpiece is RIP and OSPF (I am relying on these two to find the first job), it is true, but from the correctness of these algorithms in the process, you will find that is indeed " The most optimized route to hop is really the most optimized route for the global.

In this paper, I only give proof of the Dijkstra algorithm based on the link state routing protocol, because the link state database is the same for every device in the whole network. So it's very well understood.

The correctness of the Dijkstra algorithm proves that the correctness of the Dijkstra algorithm is proved first. Ability to carry on perhaps. After all. The Dijkstra algorithm itself, however, guides the steps in step by step, and does not prove that every path in the shortest path tree that has been so frustrating is indeed the shortest.

And to prove the principle of progressive global optimization. Need this fact.
The following gives a simple proof of the correctness of the Dijkstra algorithm, and the specific complete mathematical proof can take this idea:

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Skip-the-Hop global optimization problem The following name is the problem where the hop-by-jump global optimization is located:

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A single-hop global optimization proves that the following gives a simple proof of the global optimization of the hop-hopping. The way of proving is varied. What I'm giving you here is one of the following:

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Attached: The greedy model of the Dijkstra algorithm assumes that we pour a glass of water on the ground, observing the traces of water spreading out, and understanding the Dijkstra algorithm. It is indeed self-evident.

Nature is lazy and always acts in the most labor-saving way. The water molecule starts at the landing point, and on a bumpy ground, as gravity (which temporarily does not consider other molecular forces) reaches a series of points along a certain path, these paths must be the shortest path. We can see the rough level as a weighted path, and this is not the same algorithm model as Dijkstra?

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Principle of Internet IP-based global routing optimization-dijkstra algorithm proof