{"paper":{"title":"A Fast and Simple $(1+\\epsilon)$-Approximation for Minimum Spanning Trees in Doubling Metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christian Sohler, Di Yue, Felix Hommelsheim, Jan H\\\"ockendorff","submitted_at":"2026-07-14T21:36:53Z","abstract_excerpt":"The minimum spanning tree (MST) problem is one of the most basic optimization problems on metric spaces and graphs. We study the problem of computing a $(1+\\epsilon)$-approximation to the MST of an $n$-point metric space $(X, \\mathbf{d})$ of doubling dimension $\\mathrm{ddim}$. In doubling metrics, previous deterministic algorithms incur a running time with dependence $\\epsilon^{-O(\\mathrm{ddim})}$.\n  We give a deterministic algorithm that computes a $(1+\\epsilon)$-approximation to MST in time $2^{O(\\mathrm{ddim})} n \\bigl(\\log n + \\epsilon^{-1} \\log^4(1/\\epsilon)\\bigr)$. For bounded doubling d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13284","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.13284/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}