{"paper":{"title":"Additive Spanners and Distance Oracles in Quadratic Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mathias B{\\ae}k Tejs Knudsen","submitted_at":"2017-04-14T16:36:22Z","abstract_excerpt":"Let $G$ be an unweighted, undirected graph. An additive $k$-spanner of $G$ is a subgraph $H$ that approximates all distances between pairs of nodes up to an additive error of $+k$, that is, it satisfies $d_H(u,v) \\le d_G(u,v)+k$ for all nodes $u,v$, where $d$ is the shortest path distance. We give a deterministic algorithm that constructs an additive $O\\!\\left(1\\right)$-spanner with $O\\!\\left(n^{4/3}\\right)$ edges in $O\\!\\left(n^2\\right)$ time. This should be compared with the randomized Monte Carlo algorithm by Woodruff [ICALP 2010] giving an additive $6$-spanner with $O\\!\\left(n^{4/3}\\log^3 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04473","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"}