Suppose there exist four randomly distributed points in $n$-dimensional space: $A$, $B$, $C$, and $D$.
We have no knowledge of the coordinates of any of these points, but we do know nearly all of the distances:
$\overline{AB} = j_1$
$\overline{BD} = j_2$
$\overline{AC} = j_3$
$\overline{CD} = j_4$
We have, in other words, the distances from $A$ to $D$ via each of the other points, but not the distance $\overline{AD}$ itself (nor the distance $\overline{BC}$ between these intermediary points).
Clearly, we can't determine the precise distance $\overline{AD}$, though we can be sure that it's less than the smaller of $j_1 + j_2$ and $j_3 + j_4$.
My question is this: is there any way to go about formulating an estimate for $\overline{AD}$? How would this estimate change if we were to have more or fewer intermediary points?