Shotgun Assembly of Erdos-Renyi Random Graphs
Julia Gaudio, Elchanan Mossel

TL;DR
This paper investigates the conditions under which Erdős-Rényi random graphs can be reconstructed from local neighborhoods, identifying specific regimes of edge probability decay where reconstruction is possible or impossible.
Contribution
It provides the first rigorous analysis of graph shotgun assembly for ER random graphs, establishing thresholds for exact reconstructability based on neighborhood size and edge probability.
Findings
Reconstruction from distance-1 neighborhoods is possible for < /3.
Reconstruction from distance-2 neighborhoods is possible for < /2 and /2 < /5.
Reconstruction is impossible for higher /5 regimes.
Abstract
Graph shotgun assembly refers to the problem of reconstructing a graph from a collection of local neighborhoods. In this paper, we consider shotgun assembly of \ER random graphs , where for . We consider both reconstruction up to isomorphism as well as exact reconstruction (recovering the vertex labels as well as the structure). We show that given the collection of distance- neighborhoods, is exactly reconstructable for , but not reconstructable for . Given the collection of distance- neighborhoods, is exactly reconstructable for , but not reconstructable for .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
