{"paper":{"title":"Fast Constructions of Light-Weight Spanners for General Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael Elkin, Shay Solomon","submitted_at":"2012-07-06T15:46:23Z","abstract_excerpt":"To our knowledge, there are only two known algorithms for constructing sparse and light spanners for general graphs. One of them is the greedy algorithm of Alth$\\ddot{o}$fer et al. \\cite{ADDJS93}, analyzed by Chandra et al. in SoCG'92. The greedy algorithm consructs, for every \\emph{weighted} undirected $n$-vertex $m$-edge graph $G = (V,E)$ and any integer $k \\ge 1$, a $(2k-1)$-spanner with $O(n^{1 + 1/k})$ edges and weight $O(k \\cdot n^{(1+\\eps)/k}) \\cdot \\omega(MST(G))$, for any $\\eps > 0$. The drawback of the greedy algorithm is that it requires $O(m \\cdot (n^{1 + 1/k} + n \\cdot \\log n))$ t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1668","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"}