Given is a tree

We now include the errors in the inequality and simplify the above inequality:

where is the error in the distance measurement

If we subtract the second from the first equation, we get:

The conclusion is: we only get a wrong circular order if each of the four distances involved has an error of at least (the length of the shortest edge).

Note that this is the error if we simply take

First we have to determine the number of circular orders we have to consider. We want to find the error with respect to the shortest edge

For illustration we give a small example: let the probability