{"paper":{"title":"Solving Positive Linear Programs with Differential Privacy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Differentially private solvers for positive LPs that approximate solutions with bounded constraint violations and improve on prior instance-dependent and new data-independent guarantees.","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Adrian Vladu, Alina Ene, Huy Le Nguyen, Ta Duy Nguyen","submitted_at":"2026-04-29T16:02:03Z","abstract_excerpt":"We study differentially private approximation algorithms for positive linear programs (LPs with nonnegative coefficients and variables), focusing on the fundamental families of packing, covering, and mixed packing-covering formulations. We focus on the high-sensitivity, constraint-private regime of Hsu-Roth-Roughgarden-Ullman (ICALP 2014), where neighboring instances may differ by an arbitrary single constraint, so one cannot hope to approximately satisfy every constraint under privacy. We give private solvers that return approximate solutions while violating only a controlled number of constr"},"claims":{"count":3,"items":[{"kind":"strongest_claim","text":"We give private solvers that return approximate solutions while violating only a controlled number of constraints. Our algorithms improve the prior instance-dependent guarantees, and also yield new data-independent bounds that depend only on the dimension.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The focus on positive linear programs (nonnegative coefficients and variables) in the high-sensitivity constraint-private regime of Hsu et al., where full constraint satisfaction under privacy is impossible.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Differentially private solvers for positive LPs that approximate solutions with bounded constraint violations and improve on prior instance-dependent and new data-independent guarantees.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"}],"snapshot_sha256":"d851d18a6b368dc66eb84debe174ec9117f2bb66c3a51ccf80f7e853a6666e0a"},"source":{"id":"2604.26838","kind":"arxiv","version":2},"verdict":{"id":"0b2fbbdc-c5da-4527-9515-afff0952d944","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T12:02:13.379083Z","strongest_claim":"We give private solvers that return approximate solutions while violating only a controlled number of constraints. Our algorithms improve the prior instance-dependent guarantees, and also yield new data-independent bounds that depend only on the dimension.","one_line_summary":"Differentially private solvers for positive LPs that approximate solutions with bounded constraint violations and improve on prior instance-dependent and new data-independent guarantees.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The focus on positive linear programs (nonnegative coefficients and variables) in the high-sensitivity constraint-private regime of Hsu et al., where full constraint satisfaction under privacy is impossible.","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26838/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T23:40:36.674563Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ecec1d8ff140d5ed7b8b02c42678f1e979fe6049f9480bbe729c3ccecafc1f47"},"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"}