{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ASTISFDGPASFHCRTNK4PYSD2RY","short_pith_number":"pith:ASTISFDG","canonical_record":{"source":{"id":"1809.06506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-09-18T02:26:03Z","cross_cats_sorted":[],"title_canon_sha256":"75d8f1214aab6f557408f69815ec6b24cee580d08f321553d7bc8bb1adfef461","abstract_canon_sha256":"488cd3afe092c27cc510cae27f89c3d62a58f33ceb916e94bc61d6667bcb3fb7"},"schema_version":"1.0"},"canonical_sha256":"04a68914667824538a336ab8fc487a8e372fb69217316ff5144abc25b7216e02","source":{"kind":"arxiv","id":"1809.06506","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06506","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06506v2","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06506","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"ASTISFDGPASF","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"ASTISFDGPASFHCRT","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"ASTISFDG","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ASTISFDGPASFHCRTNK4PYSD2RY","target":"record","payload":{"canonical_record":{"source":{"id":"1809.06506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-09-18T02:26:03Z","cross_cats_sorted":[],"title_canon_sha256":"75d8f1214aab6f557408f69815ec6b24cee580d08f321553d7bc8bb1adfef461","abstract_canon_sha256":"488cd3afe092c27cc510cae27f89c3d62a58f33ceb916e94bc61d6667bcb3fb7"},"schema_version":"1.0"},"canonical_sha256":"04a68914667824538a336ab8fc487a8e372fb69217316ff5144abc25b7216e02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:27.737367Z","signature_b64":"Wdh+VOsghgQSg/leYE19LcBQj8gOrpMn84IRnoA0KgqyUQrHpRRf70OM0vjbv8/qw01uhnI5Y3QGlbOztqhKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04a68914667824538a336ab8fc487a8e372fb69217316ff5144abc25b7216e02","last_reissued_at":"2026-05-17T23:59:27.736845Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:27.736845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.06506","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MVtabPwbH5RTconh5/n7qw4W4Y6HiGZcjo50GlcL9afiVCiqZv6l4Xqxy64ZsswMlCwb2IOCb7QlqQOL5AM0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:04:48.662655Z"},"content_sha256":"225b0c8a97fd15b4766993f0693376f6d28b9df2acdcd5855e56549ba1314661","schema_version":"1.0","event_id":"sha256:225b0c8a97fd15b4766993f0693376f6d28b9df2acdcd5855e56549ba1314661"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ASTISFDGPASFHCRTNK4PYSD2RY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Partition Set Cover Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Kasturi Varadarajan, Tanmay Inamdar","submitted_at":"2018-09-18T02:26:03Z","abstract_excerpt":"Several algorithms with an approximation guarantee of $O(\\log n)$ are known for the Set Cover problem, where $n$ is the number of elements. We study a generalization of the Set Cover problem, called the Partition Set Cover problem. Here, the elements are partitioned into $r$ \\emph{color classes}, and we are required to cover at least $k_t$ elements from each color class $\\mathcal{C}_t$, using the minimum number of sets. We give a randomized LP-rounding algorithm that is an $O(\\beta + \\log r)$ approximation for the Partition Set Cover problem. Here $\\beta$ denotes the approximation guarantee fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06506","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"giyGGmtio6uKjXFMjlP1FV9fzVBgpfwZPtFBx/ULw3Op18mchBHrHaTR1jQKbdPApIpIBWQCGih1TwkfVt62BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T22:04:48.663049Z"},"content_sha256":"15e2bb1f67ecd552e46ef1e11b27452ca7be0a313e46e291c7a044df8cba5685","schema_version":"1.0","event_id":"sha256:15e2bb1f67ecd552e46ef1e11b27452ca7be0a313e46e291c7a044df8cba5685"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ASTISFDGPASFHCRTNK4PYSD2RY/bundle.json","state_url":"https://pith.science/pith/ASTISFDGPASFHCRTNK4PYSD2RY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ASTISFDGPASFHCRTNK4PYSD2RY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T22:04:48Z","links":{"resolver":"https://pith.science/pith/ASTISFDGPASFHCRTNK4PYSD2RY","bundle":"https://pith.science/pith/ASTISFDGPASFHCRTNK4PYSD2RY/bundle.json","state":"https://pith.science/pith/ASTISFDGPASFHCRTNK4PYSD2RY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ASTISFDGPASFHCRTNK4PYSD2RY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ASTISFDGPASFHCRTNK4PYSD2RY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"488cd3afe092c27cc510cae27f89c3d62a58f33ceb916e94bc61d6667bcb3fb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-09-18T02:26:03Z","title_canon_sha256":"75d8f1214aab6f557408f69815ec6b24cee580d08f321553d7bc8bb1adfef461"},"schema_version":"1.0","source":{"id":"1809.06506","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06506","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06506v2","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06506","created_at":"2026-05-17T23:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"ASTISFDGPASF","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"ASTISFDGPASFHCRT","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"ASTISFDG","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:15e2bb1f67ecd552e46ef1e11b27452ca7be0a313e46e291c7a044df8cba5685","target":"graph","created_at":"2026-05-17T23:59:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Several algorithms with an approximation guarantee of $O(\\log n)$ are known for the Set Cover problem, where $n$ is the number of elements. We study a generalization of the Set Cover problem, called the Partition Set Cover problem. Here, the elements are partitioned into $r$ \\emph{color classes}, and we are required to cover at least $k_t$ elements from each color class $\\mathcal{C}_t$, using the minimum number of sets. We give a randomized LP-rounding algorithm that is an $O(\\beta + \\log r)$ approximation for the Partition Set Cover problem. Here $\\beta$ denotes the approximation guarantee fo","authors_text":"Kasturi Varadarajan, Tanmay Inamdar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-09-18T02:26:03Z","title":"On the Partition Set Cover Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06506","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:225b0c8a97fd15b4766993f0693376f6d28b9df2acdcd5855e56549ba1314661","target":"record","created_at":"2026-05-17T23:59:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"488cd3afe092c27cc510cae27f89c3d62a58f33ceb916e94bc61d6667bcb3fb7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-09-18T02:26:03Z","title_canon_sha256":"75d8f1214aab6f557408f69815ec6b24cee580d08f321553d7bc8bb1adfef461"},"schema_version":"1.0","source":{"id":"1809.06506","kind":"arxiv","version":2}},"canonical_sha256":"04a68914667824538a336ab8fc487a8e372fb69217316ff5144abc25b7216e02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04a68914667824538a336ab8fc487a8e372fb69217316ff5144abc25b7216e02","first_computed_at":"2026-05-17T23:59:27.736845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:27.736845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wdh+VOsghgQSg/leYE19LcBQj8gOrpMn84IRnoA0KgqyUQrHpRRf70OM0vjbv8/qw01uhnI5Y3QGlbOztqhKDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:27.737367Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.06506","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:225b0c8a97fd15b4766993f0693376f6d28b9df2acdcd5855e56549ba1314661","sha256:15e2bb1f67ecd552e46ef1e11b27452ca7be0a313e46e291c7a044df8cba5685"],"state_sha256":"a04fa9d569d441a1f2fce19b16f589c6021ca759212bd4192c0aefebc52472f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"coBFomkrskNbRJwh69B8VwO7LwDUOj5rKF9Yzb3rhfTvt1SSpN1dMiF5rnuEO34E612AMebn3RE5lAqVY+cKCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T22:04:48.666594Z","bundle_sha256":"8ad325047c6fcfbd51a5b1364dd02cb37e716d6627b542dea31ec6c87f4858b3"}}