{"paper":{"title":"Covering Points with Rectangular Boundaries","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Daniel Lokshtanov, Kushal Singanporia, Madhumita Kundu, Saket Saurabh, Soumi Nandi","submitted_at":"2026-07-09T07:30:08Z","abstract_excerpt":"Geometric covering problems ask for a small family of geometric objects whose union covers a given point set. We study the more restrictive \\emph{boundary covering} variant, where every point must lie on the boundary of a chosen object. Motivated by the framework of Langerman and Morin\\,[Discret.\\ Comput.\\ Geom., 2005] for hyperspheres, we initiate the study of boundary covering by axis-parallel rectangles.\n  We first consider the \\emph{discrete} setting, where rectangles must be selected from a given family. We define \\bcdaprfull\\ (\\bcdaprshort): given a point set \\(P\\subseteq\\mathbb{R}^2\\), "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08183","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/2607.08183/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"}