{"paper":{"title":"Linear-Size Hopsets with Small Hopbound, and Distributed Routing with Low Memory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael Elkin, Ofer Neiman","submitted_at":"2017-04-27T08:08:22Z","abstract_excerpt":"For a positive parameter $\\beta$, the $\\beta$-bounded distance between a pair of vertices $u,v$ in a weighted undirected graph $G = (V,E,\\omega)$ is the length of the shortest $u-v$ path in $G$ with at most $\\beta$ edges, aka {\\em hops}. For $\\beta$ as above and $\\epsilon>0$, a {\\em $(\\beta,\\epsilon)$-hopset} of $G = (V,E,\\omega)$ is a graph $G' =(V,H,\\omega_H)$ on the same vertex set, such that all distances in $G$ are $(1+\\epsilon)$-approximated by $\\beta$-bounded distances in $G\\cup G'$.\n  Hopsets are a fundamental graph-theoretic and graph-algorithmic construct, and they are widely used fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08468","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"}