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Range counting for different range spaces is a central problem in Computational Geometry.\n  We study $(\\epsilon, \\delta)$-differentially private algorithms for range counting. Our main results are for the range space given by hyperplanes, that is, the halfspace counting problem. We present an $(\\epsi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1203.5453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-03-24T22:25:12Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"c2e80c1535fe788f651ec667565ff7a7de5d0d4d13e7615b1e1ebe22e01f47c3","abstract_canon_sha256":"5750eb22a44ac97ba90dd0850bbd72b91eecd6e40ba38c1321371fd6d7fe252e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:15.029203Z","signature_b64":"7hFNPGgdY55lOjbgZvuPlzZ+8jHaNxEORQjcpZmXeNAq2tGw9vZMYCErw6qx/KxVO7QiZXmrRTnuCam/0T+kCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b0349b8031272380ce13bc98107548a30f6e156e61d6d521b4186faf2d393cc","last_reissued_at":"2026-05-18T03:59:15.028487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:15.028487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Private Halfspace Counting via Discrepancy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Aleksandar Nikolov, S. Muthukrishnan","submitted_at":"2012-03-24T22:25:12Z","abstract_excerpt":"A range counting problem is specified by a set $P$ of size $|P| = n$ of points in $\\mathbb{R}^d$, an integer weight $x_p$ associated to each point $p \\in P$, and a range space ${\\cal R} \\subseteq 2^{P}$. Given a query range $R \\in {\\cal R}$, the target output is $R(\\vec{x}) = \\sum_{p \\in R}{x_p}$. Range counting for different range spaces is a central problem in Computational Geometry.\n  We study $(\\epsilon, \\delta)$-differentially private algorithms for range counting. Our main results are for the range space given by hyperplanes, that is, the halfspace counting problem. 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