{"paper":{"title":"Convex Set Disjointness, Distributed Learning of Halfspaces, and LP Feasibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CG","cs.DM","cs.LG"],"primary_cat":"cs.DS","authors_text":"Gillat Kol, Mark Braverman, Raghuvansh R. Saxena, Shay Moran","submitted_at":"2019-09-08T21:19:34Z","abstract_excerpt":"We study the Convex Set Disjointness (CSD) problem, where two players have input sets taken from an arbitrary fixed domain~$U\\subseteq \\mathbb{R}^d$ of size $\\lvert U\\rvert = n$. Their mutual goal is to decide using minimum communication whether the convex hulls of their sets intersect (equivalently, whether their sets can be separated by a hyperplane).\n  Different forms of this problem naturally arise in distributed learning and optimization: it is equivalent to {\\em Distributed Linear Program (LP) Feasibility} -- a basic task in distributed optimization, and it is tightly linked to {\\it Dist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.03547","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/1909.03547/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"}