{"paper":{"title":"Near-Optimal $O(k)$-Robust Geometric Spanners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Pat Morin, Paz Carmi, Prosenjit Bose, Vida Dujmovic","submitted_at":"2018-12-24T13:08:31Z","abstract_excerpt":"For any constants $d\\ge 1$, $\\epsilon >0$, $t>1$, and any $n$-point set $P\\subset\\mathbb{R}^d$, we show that there is a geometric graph $G=(P,E)$ having $O(n\\log^2 n\\log\\log n)$ edges with the following property: For any $F\\subseteq P$, there exists $F^+\\supseteq F$, $|F^+| \\le (1+\\epsilon)|F|$ such that, for any pair $p,q\\in P\\setminus F^+$, the graph $G-F$ contains a path from $p$ to $q$ whose (Euclidean) length is at most $t$ times the Euclidean distance between $p$ and $q$.\n  In the terminology of robust spanners (Bose \\et al, SICOMP, 42(4):1720--1736, 2013) the graph $G$ is a $(1+\\epsilon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09913","kind":"arxiv","version":2},"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"}