{"paper":{"title":"Multivariate Exploration of Metric Dilation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","math.CO"],"primary_cat":"cs.DM","authors_text":"Aritra Banik, Fedor V. Fomin, Petr A. Golovach, Saket Saurabh, Satyabrata Jana, Tanmay Inamdar","submitted_at":"2025-01-08T15:05:14Z","abstract_excerpt":"Let $G$ be a weighted graph embedded in a metric space $(M, d_M )$. The vertices of $G$ correspond to the points in $M$ , with the weight of each edge $uv$ being the distance $d_M (u, v)$ between their respective points in $M$ . The dilation (or stretch) of $G$ is defined as the minimum factor $t$ such that, for any pair of vertices $u, v$, the distance between $u$ and $v$-represented by the weight of a shortest $u$, $v$-path is at most $ t \\cdot d_M (u, v)$. We study Dilation t-Augmentation, where the objective is, given a metric $M $, a graph $G$, and numerical values $k$ and $t$, to determi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04555","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/2501.04555/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"}