Let V be a set of n points on the real line. Suppose that each pairwise
distance is known independently with probability p. How much of V can be
reconstructed up to isometry?
We prove that p=(logn)/n is a sharp threshold for reconstructing all of
V which improves a result of Benjamini and Tzalik. This follows from a
hitting time result for the random process where the pairwise distances are
revealed one-by-one uniformly at random. We also show that 1/n is a weak
threshold for reconstructing a linear proportion of V.Comment: 13 page