{"paper":{"title":"From Hierarchical Partitions to Hierarchical Covers: Optimal Fault-Tolerant Spanners for Doubling Metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Shay Solomon","submitted_at":"2013-04-30T19:58:41Z","abstract_excerpt":"In this paper we devise an optimal construction of fault-tolerant spanners for doubling metrics. Specifically, for any $n$-point doubling metric, any $\\eps > 0$, and any integer $0 \\le k \\le n-2$, our construction provides a $k$-fault-tolerant $(1+\\eps)$-spanner with optimal degree $O(k)$ within optimal time $O(n \\log n + k n)$.\n  We then strengthen this result to provide near-optimal (up to a factor of $\\log k$) guarantees on the diameter and weight of our spanners, namely, diameter $O(\\log n)$ and weight $O(k^2 + k \\log n) \\cdot \\omega(MST)$, while preserving the optimal guarantees on the de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.8135","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"}