Relative positions on a line are uniquely recoverable from connected collision graphs under full observability, via layer decompositions into maximal cliques for partial data, and NP-hard graph completion for incomplete observations.
Transitive orientation of graphs and identification of permutation graphs
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Positional Identifiability from Pairwise Collision Data
Relative positions on a line are uniquely recoverable from connected collision graphs under full observability, via layer decompositions into maximal cliques for partial data, and NP-hard graph completion for incomplete observations.