{"paper":{"title":"Balancing Degree, Diameter and Weight in Euclidean Spanners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Michael Elkin, Shay Solomon","submitted_at":"2011-08-30T17:49:19Z","abstract_excerpt":"In this paper we devise a novel \\emph{unified} construction of Euclidean spanners that trades between the maximum degree, diameter and weight gracefully. For a positive integer k, our construction provides a (1+eps)-spanner with maximum degree O(k), diameter O(log_k n + alpha(k)), weight O(k \\cdot log_k n \\cdot log n) \\cdot w(MST(S)), and O(n) edges. Note that for k= n^{1/alpha(n)} this gives rise to diameter O(alpha(n)), weight O(n^{1/alpha(n)} \\cdot log n \\cdot alpha(n)) \\cdot w(MST(S)) and maximum degree O(n^{1/alpha(n)}), which improves upon a classical result of Arya et al. \\cite{ADMSS95}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6022","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"}