{"paper":{"title":"Thorup-Zwick Emulators are Universally Optimal Hopsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Seth Pettie, Shang-En Huang","submitted_at":"2017-04-30T15:34:02Z","abstract_excerpt":"A $(\\beta,\\epsilon)$-$\\textit{hopset}$ is, informally, a weighted edge set that, when added to a graph, allows one to get from point $a$ to point $b$ using a path with at most $\\beta$ edges (\"hops\") and length $(1+\\epsilon)\\mathrm{dist}(a,b)$. In this paper we observe that Thorup and Zwick's $\\textit{sublinear additive}$ emulators are also actually $(O(k/\\epsilon)^k,\\epsilon)$-hopsets for every $\\epsilon>0$, and that with a small change to the Thorup-Zwick construction, the size of the hopset can be made $O(n^{1+\\frac{1}{2^{k+1}-1}})$. As corollaries, we also shave \"$k$\" factors off the size o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00327","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":""},"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"}