{"paper":{"title":"Sparse Bounded Hop-Spanners for Geometric Intersection Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CG","authors_text":"Csaba D. Toth, Shakhar Smorodinsky, Sujoy Bhore, Timothy M. Chan, Zhengcheng Huang","submitted_at":"2025-04-08T09:40:14Z","abstract_excerpt":"We present new results on $2$- and $3$-hop spanners for geometric intersection graphs. These include improved upper and lower bounds for $2$- and $3$-hop spanners for many geometric intersection graphs in $\\mathbb{R}^d$. For example, we show that the intersection graph of $n$ balls in $\\mathbb{R}^d$ admits a $2$-hop spanner of size $O^*\\left(n^{\\frac{3}{2}-\\frac{1}{2(2\\lfloor d/2\\rfloor +1)}}\\right)$ and the intersection graph of $n$ fat axis-parallel boxes in $\\mathbb{R}^d$ admits a $2$-hop spanner of size $O(n \\log^{d+1}n)$.\n  Furthermore, we show that the intersection graph of general semi-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.05861","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/2504.05861/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"}