Work

Reconstructing a point set from a random subset of its pairwise distances

Year: 2024

Type: article

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

Source: UCL Discovery (University College London)

Authors: Illingworth, Frederick, Girao, Antonio, Michel, Lukas, Powierski, Emil, Scott, Alex

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6986853704

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