{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MSMICLQ73BVKZKR7XHUJ54TH23","short_pith_number":"pith:MSMICLQ7","schema_version":"1.0","canonical_sha256":"6498812e1fd86aacaa3fb9e89ef267d6ea77c79347150f6d64afda1ed090e6ab","source":{"kind":"arxiv","id":"1807.04152","version":1},"attestation_state":"computed","paper":{"title":"Integrality Gap of the Configuration LP for the Restricted Max-Min Fair Allocation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Siu-Wing Cheng, Yuchen Mao","submitted_at":"2018-07-11T14:20:48Z","abstract_excerpt":"The max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. Each player $p$ has a non-negative value $v_{pr}$ on resource $r$. In the restricted case, we have $v_{pr}\\in \\{v_r, 0\\}$. That is, a resource $r$ is worth value $v_r$ for the players who desire it and value 0 for the other players. In this paper, we consider the configuration LP, a linear programming relaxation for the restricted problem. The integrality gap of the configuration LP is at least $2$. Asadpour, Feige, and Saberi proved an upper bound of $"},"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":"1807.04152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-11T14:20:48Z","cross_cats_sorted":[],"title_canon_sha256":"6eb701002547bde82b0bc8e800b6f9ce30c44f02c1b0f399cfc934dfc5689d90","abstract_canon_sha256":"7df1afacbace5176332179a202ef701e345f8f64e985fd71a5e477a1cf4df639"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:57.814854Z","signature_b64":"iAKWWZs3wI/peGFkQ0JOcK20OZKLbS5UpNeyufoETfYveMFa6y46R8QbtkUM1ZA5/Cl3Myisp7ou+GnEDWzLAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6498812e1fd86aacaa3fb9e89ef267d6ea77c79347150f6d64afda1ed090e6ab","last_reissued_at":"2026-05-18T00:10:57.814075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:57.814075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integrality Gap of the Configuration LP for the Restricted Max-Min Fair Allocation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Siu-Wing Cheng, Yuchen Mao","submitted_at":"2018-07-11T14:20:48Z","abstract_excerpt":"The max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. Each player $p$ has a non-negative value $v_{pr}$ on resource $r$. In the restricted case, we have $v_{pr}\\in \\{v_r, 0\\}$. That is, a resource $r$ is worth value $v_r$ for the players who desire it and value 0 for the other players. In this paper, we consider the configuration LP, a linear programming relaxation for the restricted problem. The integrality gap of the configuration LP is at least $2$. Asadpour, Feige, and Saberi proved an upper bound of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04152","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":"1807.04152","created_at":"2026-05-18T00:10:57.814204+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.04152v1","created_at":"2026-05-18T00:10:57.814204+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04152","created_at":"2026-05-18T00:10:57.814204+00:00"},{"alias_kind":"pith_short_12","alias_value":"MSMICLQ73BVK","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"MSMICLQ73BVKZKR7","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"MSMICLQ7","created_at":"2026-05-18T12:32:40.477152+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/MSMICLQ73BVKZKR7XHUJ54TH23","json":"https://pith.science/pith/MSMICLQ73BVKZKR7XHUJ54TH23.json","graph_json":"https://pith.science/api/pith-number/MSMICLQ73BVKZKR7XHUJ54TH23/graph.json","events_json":"https://pith.science/api/pith-number/MSMICLQ73BVKZKR7XHUJ54TH23/events.json","paper":"https://pith.science/paper/MSMICLQ7"},"agent_actions":{"view_html":"https://pith.science/pith/MSMICLQ73BVKZKR7XHUJ54TH23","download_json":"https://pith.science/pith/MSMICLQ73BVKZKR7XHUJ54TH23.json","view_paper":"https://pith.science/paper/MSMICLQ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.04152&json=true","fetch_graph":"https://pith.science/api/pith-number/MSMICLQ73BVKZKR7XHUJ54TH23/graph.json","fetch_events":"https://pith.science/api/pith-number/MSMICLQ73BVKZKR7XHUJ54TH23/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MSMICLQ73BVKZKR7XHUJ54TH23/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MSMICLQ73BVKZKR7XHUJ54TH23/action/storage_attestation","attest_author":"https://pith.science/pith/MSMICLQ73BVKZKR7XHUJ54TH23/action/author_attestation","sign_citation":"https://pith.science/pith/MSMICLQ73BVKZKR7XHUJ54TH23/action/citation_signature","submit_replication":"https://pith.science/pith/MSMICLQ73BVKZKR7XHUJ54TH23/action/replication_record"}},"created_at":"2026-05-18T00:10:57.814204+00:00","updated_at":"2026-05-18T00:10:57.814204+00:00"}