{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VSF6FIPGJUHL5KVUPE4LN2HF2L","short_pith_number":"pith:VSF6FIPG","schema_version":"1.0","canonical_sha256":"ac8be2a1e64d0ebeaab47938b6e8e5d2cd4f2d98fd3937a301184798cbeb8639","source":{"kind":"arxiv","id":"1507.08501","version":1},"attestation_state":"computed","paper":{"title":"Randomised Rounding with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dhiraj Madan, Sandeep Sen","submitted_at":"2015-07-30T13:47:09Z","abstract_excerpt":"We develop new techniques for rounding packing integer programs using iterative randomized rounding. It is based on a novel application of multidimensional Brownian motion in $\\mathbb{R}^n$. Let $\\overset{\\sim}{x} \\in {[0,1]}^n$ be a fractional feasible solution of a packing constraint $A x \\leq 1,\\ \\ $ $A \\in {\\{0,1 \\}}^{m\\times n}$ that maximizes a linear objective function. The independent randomized rounding method of Raghavan-Thompson rounds each variable $x_i$ to 1 with probability $\\overset{\\sim}{x_i}$ and 0 otherwise. The expected value of the rounded objective function matches the fra"},"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":"1507.08501","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-30T13:47:09Z","cross_cats_sorted":[],"title_canon_sha256":"0ea32c5600af4991d12d57cbedc953e72636097fe33018994072cf02fe4eaf40","abstract_canon_sha256":"8d41dd6f0c8e670ae0a1774e57dcfa2ecad40f51f40626ad507263bc7efacb18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:06.242681Z","signature_b64":"ocj9Znhw8OVeeeWVYy3QnrPJ9ncdzxQaW5tkSwiWIxddm8PlT+7GQnxRFwl9khxDFqgjjDzxAiheezPPUC71BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac8be2a1e64d0ebeaab47938b6e8e5d2cd4f2d98fd3937a301184798cbeb8639","last_reissued_at":"2026-05-18T01:36:06.242116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:06.242116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Randomised Rounding with Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dhiraj Madan, Sandeep Sen","submitted_at":"2015-07-30T13:47:09Z","abstract_excerpt":"We develop new techniques for rounding packing integer programs using iterative randomized rounding. It is based on a novel application of multidimensional Brownian motion in $\\mathbb{R}^n$. Let $\\overset{\\sim}{x} \\in {[0,1]}^n$ be a fractional feasible solution of a packing constraint $A x \\leq 1,\\ \\ $ $A \\in {\\{0,1 \\}}^{m\\times n}$ that maximizes a linear objective function. The independent randomized rounding method of Raghavan-Thompson rounds each variable $x_i$ to 1 with probability $\\overset{\\sim}{x_i}$ and 0 otherwise. The expected value of the rounded objective function matches the fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08501","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":""},"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":"1507.08501","created_at":"2026-05-18T01:36:06.242188+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.08501v1","created_at":"2026-05-18T01:36:06.242188+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08501","created_at":"2026-05-18T01:36:06.242188+00:00"},{"alias_kind":"pith_short_12","alias_value":"VSF6FIPGJUHL","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"VSF6FIPGJUHL5KVU","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"VSF6FIPG","created_at":"2026-05-18T12:29:47.479230+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/VSF6FIPGJUHL5KVUPE4LN2HF2L","json":"https://pith.science/pith/VSF6FIPGJUHL5KVUPE4LN2HF2L.json","graph_json":"https://pith.science/api/pith-number/VSF6FIPGJUHL5KVUPE4LN2HF2L/graph.json","events_json":"https://pith.science/api/pith-number/VSF6FIPGJUHL5KVUPE4LN2HF2L/events.json","paper":"https://pith.science/paper/VSF6FIPG"},"agent_actions":{"view_html":"https://pith.science/pith/VSF6FIPGJUHL5KVUPE4LN2HF2L","download_json":"https://pith.science/pith/VSF6FIPGJUHL5KVUPE4LN2HF2L.json","view_paper":"https://pith.science/paper/VSF6FIPG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.08501&json=true","fetch_graph":"https://pith.science/api/pith-number/VSF6FIPGJUHL5KVUPE4LN2HF2L/graph.json","fetch_events":"https://pith.science/api/pith-number/VSF6FIPGJUHL5KVUPE4LN2HF2L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VSF6FIPGJUHL5KVUPE4LN2HF2L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VSF6FIPGJUHL5KVUPE4LN2HF2L/action/storage_attestation","attest_author":"https://pith.science/pith/VSF6FIPGJUHL5KVUPE4LN2HF2L/action/author_attestation","sign_citation":"https://pith.science/pith/VSF6FIPGJUHL5KVUPE4LN2HF2L/action/citation_signature","submit_replication":"https://pith.science/pith/VSF6FIPGJUHL5KVUPE4LN2HF2L/action/replication_record"}},"created_at":"2026-05-18T01:36:06.242188+00:00","updated_at":"2026-05-18T01:36:06.242188+00:00"}