{"paper":{"title":"Metric Decompositions of Path-Separable Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Lior Kamma, Robert Krauthgamer","submitted_at":"2015-04-27T10:48:12Z","abstract_excerpt":"A prominent tool in many problems involving metric spaces is a notion of randomized low-diameter decomposition. Loosely speaking, $\\beta$-decomposition refers to a probability distribution over partitions of the metric into sets of low diameter, such that nearby points (parameterized by $\\beta>0$) are likely to be \"clustered\" together. Applying this notion to the shortest-path metric in edge-weighted graphs, it is known that $n$-vertex graphs admit an $O(\\ln n)$-padded decomposition (Bartal, 1996), and that excluded-minor graphs admit $O(1)$-padded decomposition (Klein, Plotkin and Rao 1993, F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07019","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"}