{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GBKGXM5HQCSFPW6YILOI2VEM3C","short_pith_number":"pith:GBKGXM5H","canonical_record":{"source":{"id":"1704.05384","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-18T15:01:09Z","cross_cats_sorted":[],"title_canon_sha256":"53f7375bf9bbb73e036890fdabba73958e1a25649110e1404e58215d187068f4","abstract_canon_sha256":"9e7de813ced4bf0faa5e362d06319cf93437ae99d5da55836e04c6cf4e79ce58"},"schema_version":"1.0"},"canonical_sha256":"30546bb3a780a457dbd842dc8d548cd892c738a2bc70c4a4cc49fe72cd704b80","source":{"kind":"arxiv","id":"1704.05384","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05384","created_at":"2026-07-05T00:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05384v2","created_at":"2026-07-05T00:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05384","created_at":"2026-07-05T00:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"GBKGXM5HQCSF","created_at":"2026-07-05T00:20:49Z"},{"alias_kind":"pith_short_16","alias_value":"GBKGXM5HQCSFPW6Y","created_at":"2026-07-05T00:20:49Z"},{"alias_kind":"pith_short_8","alias_value":"GBKGXM5H","created_at":"2026-07-05T00:20:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GBKGXM5HQCSFPW6YILOI2VEM3C","target":"record","payload":{"canonical_record":{"source":{"id":"1704.05384","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-18T15:01:09Z","cross_cats_sorted":[],"title_canon_sha256":"53f7375bf9bbb73e036890fdabba73958e1a25649110e1404e58215d187068f4","abstract_canon_sha256":"9e7de813ced4bf0faa5e362d06319cf93437ae99d5da55836e04c6cf4e79ce58"},"schema_version":"1.0"},"canonical_sha256":"30546bb3a780a457dbd842dc8d548cd892c738a2bc70c4a4cc49fe72cd704b80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:20:49.882578Z","signature_b64":"E4jr75EsS2JRbP7zX5io3Yxu4biZ9Qhzc543tGIz2+1VIv0tBdOV6DzBr2wlJWpZgWFEJ4Bltu1O/VALh4RWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30546bb3a780a457dbd842dc8d548cd892c738a2bc70c4a4cc49fe72cd704b80","last_reissued_at":"2026-07-05T00:20:49.882141Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:20:49.882141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.05384","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":"2026-07-05T00:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qJ1UU3Njx8IEqrweEHbWEIO3tbAoC5Wo96fNmgX+25Ey06D6rnplnO0L48tgjxXHIKsFqydeDmU5wzhWJyfrBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T07:03:59.656690Z"},"content_sha256":"fb2b3983f53d578c337939fff978f4ae78b3e4400e80a79a41d14213feb743ba","schema_version":"1.0","event_id":"sha256:fb2b3983f53d578c337939fff978f4ae78b3e4400e80a79a41d14213feb743ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GBKGXM5HQCSFPW6YILOI2VEM3C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Online Weighted Matching: Breaking the $\\frac{1}{2}$ Barrier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Matthew Fahrbach, Morteza Zadimoghaddam","submitted_at":"2017-04-18T15:01:09Z","abstract_excerpt":"Online matching and its variants are some of the most fundamental problems in the online algorithms literature. In this paper, we study the online weighted bipartite matching problem. Karp et al. (STOC 1990) gave an elegant algorithm in the unweighted case that achieves a tight competitive ratio of $1-1/e$. In the weighted case, however, we can easily show that no competitive ratio is obtainable without the commonly accepted free disposal assumption. Under this assumption, it is not hard to prove that the greedy algorithm is $1/2$ competitive, and that this is tight for deterministic algorithm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05384","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1704.05384/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6wXo3sHJVjPfYF4JGgIjeagxYJ1JCdFHhHt1MZiHyxK3zYYYkuWIQth18H8Y7u5y+LmeuPZPRx1R1JQ8w37aAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T07:03:59.657181Z"},"content_sha256":"6e164d4468d30583a626b0645518cdd2fd4a160dd39c13a21de2480bc0d81e3e","schema_version":"1.0","event_id":"sha256:6e164d4468d30583a626b0645518cdd2fd4a160dd39c13a21de2480bc0d81e3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GBKGXM5HQCSFPW6YILOI2VEM3C/bundle.json","state_url":"https://pith.science/pith/GBKGXM5HQCSFPW6YILOI2VEM3C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GBKGXM5HQCSFPW6YILOI2VEM3C/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":"2026-08-01T07:03:59Z","links":{"resolver":"https://pith.science/pith/GBKGXM5HQCSFPW6YILOI2VEM3C","bundle":"https://pith.science/pith/GBKGXM5HQCSFPW6YILOI2VEM3C/bundle.json","state":"https://pith.science/pith/GBKGXM5HQCSFPW6YILOI2VEM3C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GBKGXM5HQCSFPW6YILOI2VEM3C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GBKGXM5HQCSFPW6YILOI2VEM3C","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":"9e7de813ced4bf0faa5e362d06319cf93437ae99d5da55836e04c6cf4e79ce58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-18T15:01:09Z","title_canon_sha256":"53f7375bf9bbb73e036890fdabba73958e1a25649110e1404e58215d187068f4"},"schema_version":"1.0","source":{"id":"1704.05384","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05384","created_at":"2026-07-05T00:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05384v2","created_at":"2026-07-05T00:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05384","created_at":"2026-07-05T00:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"GBKGXM5HQCSF","created_at":"2026-07-05T00:20:49Z"},{"alias_kind":"pith_short_16","alias_value":"GBKGXM5HQCSFPW6Y","created_at":"2026-07-05T00:20:49Z"},{"alias_kind":"pith_short_8","alias_value":"GBKGXM5H","created_at":"2026-07-05T00:20:49Z"}],"graph_snapshots":[{"event_id":"sha256:6e164d4468d30583a626b0645518cdd2fd4a160dd39c13a21de2480bc0d81e3e","target":"graph","created_at":"2026-07-05T00:20:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1704.05384/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Online matching and its variants are some of the most fundamental problems in the online algorithms literature. In this paper, we study the online weighted bipartite matching problem. Karp et al. (STOC 1990) gave an elegant algorithm in the unweighted case that achieves a tight competitive ratio of $1-1/e$. In the weighted case, however, we can easily show that no competitive ratio is obtainable without the commonly accepted free disposal assumption. Under this assumption, it is not hard to prove that the greedy algorithm is $1/2$ competitive, and that this is tight for deterministic algorithm","authors_text":"Matthew Fahrbach, Morteza Zadimoghaddam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-18T15:01:09Z","title":"Online Weighted Matching: Breaking the $\\frac{1}{2}$ Barrier"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05384","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:fb2b3983f53d578c337939fff978f4ae78b3e4400e80a79a41d14213feb743ba","target":"record","created_at":"2026-07-05T00:20:49Z","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":"9e7de813ced4bf0faa5e362d06319cf93437ae99d5da55836e04c6cf4e79ce58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-18T15:01:09Z","title_canon_sha256":"53f7375bf9bbb73e036890fdabba73958e1a25649110e1404e58215d187068f4"},"schema_version":"1.0","source":{"id":"1704.05384","kind":"arxiv","version":2}},"canonical_sha256":"30546bb3a780a457dbd842dc8d548cd892c738a2bc70c4a4cc49fe72cd704b80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30546bb3a780a457dbd842dc8d548cd892c738a2bc70c4a4cc49fe72cd704b80","first_computed_at":"2026-07-05T00:20:49.882141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:20:49.882141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E4jr75EsS2JRbP7zX5io3Yxu4biZ9Qhzc543tGIz2+1VIv0tBdOV6DzBr2wlJWpZgWFEJ4Bltu1O/VALh4RWCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:20:49.882578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05384","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb2b3983f53d578c337939fff978f4ae78b3e4400e80a79a41d14213feb743ba","sha256:6e164d4468d30583a626b0645518cdd2fd4a160dd39c13a21de2480bc0d81e3e"],"state_sha256":"bc9d0affae1993f9237f7f3442419ab8ee18db329eb713a20e1fc0b999c977cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VkLvzfKO/LOfvkyy1mIGjIc3k0nBUS1vvGIsGnK2sSyEgW2ASE1tp6/VAziwv0xCOz5k0FIgUhBC3/LfgXzVCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T07:03:59.660606Z","bundle_sha256":"70e98462e7f38fe0c8e936e216ac1fb4a9a39f288d30e9536291f72eb5b53ab5"}}