{"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"}