Triangle inequality

Creator
Creator
Seonglae Cho
Created
Created
2022 Feb 22 1:2
Editor
Edited
Edited
2025 Apr 27 9:54

Theorem

For all u,v,xV,we have δ(u,v)δ(u,x)+δ(x,v)\text{For all } u, v, x \in V , \text{we have } \newline \delta(u, v) \le \delta(u,x)+ \delta(x,v)
notion image
This means that if going through an intermediate point creates a longer path than the direct route, that path cannot be the shortest path and therefore does not need to be considered when finding the shortest path.
 
 
 
 
 
 

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