{"paper":{"title":"Directed Spanners via Flow-Based Linear Programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael Dinitz, Robert Krauthgamer","submitted_at":"2010-11-16T14:14:17Z","abstract_excerpt":"We examine directed spanners through flow-based linear programming relaxations. We design an $\\~O(n^{2/3})$-approximation algorithm for the directed $k$-spanner problem that works for all $k\\geq 1$, which is the first sublinear approximation for arbitrary edge-lengths. Even in the more restricted setting of unit edge-lengths, our algorithm improves over the previous $\\~O(n^{1-1/k})$ approximation of Bhattacharyya et al. when $k\\ge 4$. For the special case of $k=3$ we design a different algorithm achieving an $\\~O(\\sqrt{n})$-approximation, improving the previous $\\~O(n^{2/3})$. Both of our algo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3701","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"}