While star-gazing I tried to pick out some constellations and had difficulty identifying the correct sets of stars based on the shape alone. There were lots of stars that could have been as easily selected to make the right "shape"; some cloud cover might have also covered the "right" stars from view.
I wondered how specific the inter-star distances are in identifying the correct set of stars that belong to a constellation?
Explicitly, say there are 5 stars $A, B, C, D, E$ that belong to a constellation. And we knew the distance matrix between them:
A B C D E
A 0 3 4 5 7
B 3 0 2 2 3
C 4 2 0 1 3
D 5 2 1 0 2
E 7 3 3 2 0
We observe 3 stars (say, A, D, E) that are fit this set of distances exactly {$5, 2$}. Is there an information-theoretic measure that describes the specificity of this observation? How many stars can we "skip" before we are no longer confident in this observation? Are there similar error-correcting codes based on this distance principle?