{"paper":{"title":"$\\mathcal{O}(k)$-robust spanners in one dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"D\\'aniel Ol\\'ah, Kevin Buchin, Tim Hulshof","submitted_at":"2018-03-23T10:30:51Z","abstract_excerpt":"A geometric $t$-spanner on a set of points in Euclidean space is a graph containing for every pair of points a path of length at most $t$ times the Euclidean distance between the points. Informally, a spanner is $\\mathcal{O}(k)$-robust if deleting $k$ vertices only harms $\\mathcal{O}(k)$ other vertices. We show that on any one-dimensional set of $n$ points, for any $\\varepsilon>0$, there exists an $\\mathcal{O}(k)$-robust $1$-spanner with $\\mathcal{O}(n^{1+\\varepsilon})$ edges. Previously it was only known that $\\mathcal{O}(k)$-robust spanners with $\\mathcal{O}(n^2)$ edges exists and that there"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08719","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}