{"paper":{"title":"Cutting corners cheaply, or how to remove Steiner points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Huy L. Nguyen, Lior Kamma, Robert Krauthgamer","submitted_at":"2013-04-04T17:55:24Z","abstract_excerpt":"Our main result is that the Steiner Point Removal (SPR) problem can always be solved with polylogarithmic distortion, which answers in the affirmative a question posed by Chan, Xia, Konjevod, and Richa (2006). Specifically, we prove that for every edge-weighted graph $G = (V,E,w)$ and a subset of terminals $T \\subseteq V$, there is a graph $G'=(T,E',w')$ that is isomorphic to a minor of $G$, such that for every two terminals $u,v\\in T$, the shortest-path distances between them in $G$ and in $G'$ satisfy $d_{G,w}(u,v) \\le d_{G',w'}(u,v) \\le O(\\log^5|T|) \\cdot d_{G,w}(u,v)$. Our existence proof "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1449","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"}