{"paper":{"title":"Streaming Facility Location in High Dimension via Geometric Hashing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Arnold Filtser, Artur Czumaj, Mingwei Yang, Pavel Vesel\\'y, Robert Krauthgamer, Shaofeng H.-C. Jiang","submitted_at":"2022-04-05T10:12:00Z","abstract_excerpt":"In Euclidean Uniform Facility Location (UFL), the input is a set of clients in $\\mathbb{R}^d$ and the goal is to place facilities to serve them, so as to minimize the total cost of opening facilities plus connecting the clients. We study the setting of dynamic geometric streams, where the clients are presented as a sequence of insertions and deletions of points in the grid $\\{1,\\ldots,\\Delta\\}^d$, and we focus on the \\emph{high-dimensional regime}, where the algorithm must use space polynomial in $d\\cdot\\log\\Delta$.\n  We present a new algorithmic framework, based on importance sampling, for $O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.02095","kind":"arxiv","version":5},"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/2204.02095/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"}