{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SH7NTSFUNJXRS2UDJHYDRNXSMS","short_pith_number":"pith:SH7NTSFU","schema_version":"1.0","canonical_sha256":"91fed9c8b46a6f196a8349f038b6f264ba49451709289e55d67cf830feb9b254","source":{"kind":"arxiv","id":"1601.03311","version":2},"attestation_state":"computed","paper":{"title":"Improved Algorithmic Bounds for Discrepancy of Sparse Set Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Nikhil Bansal, Shashwat Garg","submitted_at":"2016-01-13T16:48:59Z","abstract_excerpt":"We consider the problem of finding a low discrepancy coloring for sparse set systems where each element lies in at most $t$ sets. We give an algorithm that finds a coloring with discrepancy $O((t \\log n \\log s)^{1/2})$ where $s$ is the maximum cardinality of a set. This improves upon the previous constructive bound of $O(t^{1/2} \\log n)$ based on algorithmic variants of the partial coloring method, and for small $s$ (e.g.$s=\\textrm{poly}(t)$) comes close to the non-constructive $O((t \\log n)^{1/2})$ bound due to Banaszczyk. Previously, no algorithmic results better than $O(t^{1/2}\\log n)$ were"},"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":"1601.03311","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-01-13T16:48:59Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"6ce4c603c1035b70c2fed91ce3f40ef9a4163e8fc10bd8419b3f1fd4b523bbef","abstract_canon_sha256":"362f251c15b13f4697c197c04a6bd5ae212c76d5b3b405dcc3b73e872a029983"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:25.306387Z","signature_b64":"LmTAJafbS2ve/qG3Xzo6A+dNEE4M7eVVW5Im6d/RZCeDCR5HloQAStToKyIItaLHjAInRSM2b/wChxO+dsfdAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91fed9c8b46a6f196a8349f038b6f264ba49451709289e55d67cf830feb9b254","last_reissued_at":"2026-05-18T01:21:25.305669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:25.305669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved Algorithmic Bounds for Discrepancy of Sparse Set Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Nikhil Bansal, Shashwat Garg","submitted_at":"2016-01-13T16:48:59Z","abstract_excerpt":"We consider the problem of finding a low discrepancy coloring for sparse set systems where each element lies in at most $t$ sets. We give an algorithm that finds a coloring with discrepancy $O((t \\log n \\log s)^{1/2})$ where $s$ is the maximum cardinality of a set. This improves upon the previous constructive bound of $O(t^{1/2} \\log n)$ based on algorithmic variants of the partial coloring method, and for small $s$ (e.g.$s=\\textrm{poly}(t)$) comes close to the non-constructive $O((t \\log n)^{1/2})$ bound due to Banaszczyk. Previously, no algorithmic results better than $O(t^{1/2}\\log n)$ were"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03311","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1601.03311","created_at":"2026-05-18T01:21:25.305796+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.03311v2","created_at":"2026-05-18T01:21:25.305796+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03311","created_at":"2026-05-18T01:21:25.305796+00:00"},{"alias_kind":"pith_short_12","alias_value":"SH7NTSFUNJXR","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SH7NTSFUNJXRS2UD","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SH7NTSFU","created_at":"2026-05-18T12:30:44.179134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SH7NTSFUNJXRS2UDJHYDRNXSMS","json":"https://pith.science/pith/SH7NTSFUNJXRS2UDJHYDRNXSMS.json","graph_json":"https://pith.science/api/pith-number/SH7NTSFUNJXRS2UDJHYDRNXSMS/graph.json","events_json":"https://pith.science/api/pith-number/SH7NTSFUNJXRS2UDJHYDRNXSMS/events.json","paper":"https://pith.science/paper/SH7NTSFU"},"agent_actions":{"view_html":"https://pith.science/pith/SH7NTSFUNJXRS2UDJHYDRNXSMS","download_json":"https://pith.science/pith/SH7NTSFUNJXRS2UDJHYDRNXSMS.json","view_paper":"https://pith.science/paper/SH7NTSFU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.03311&json=true","fetch_graph":"https://pith.science/api/pith-number/SH7NTSFUNJXRS2UDJHYDRNXSMS/graph.json","fetch_events":"https://pith.science/api/pith-number/SH7NTSFUNJXRS2UDJHYDRNXSMS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SH7NTSFUNJXRS2UDJHYDRNXSMS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SH7NTSFUNJXRS2UDJHYDRNXSMS/action/storage_attestation","attest_author":"https://pith.science/pith/SH7NTSFUNJXRS2UDJHYDRNXSMS/action/author_attestation","sign_citation":"https://pith.science/pith/SH7NTSFUNJXRS2UDJHYDRNXSMS/action/citation_signature","submit_replication":"https://pith.science/pith/SH7NTSFUNJXRS2UDJHYDRNXSMS/action/replication_record"}},"created_at":"2026-05-18T01:21:25.305796+00:00","updated_at":"2026-05-18T01:21:25.305796+00:00"}