{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GY64EC7FEETXGKUDNFGUMVE2NW","short_pith_number":"pith:GY64EC7F","canonical_record":{"source":{"id":"1809.08453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-09-22T16:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"10853333f09587d719e1c90d270f1bb5dad8d6cccf832f96505430e2e8513762","abstract_canon_sha256":"6439d2115c29f871cda21009ca2d07cc143802cefd0cd472350e6a30bba81263"},"schema_version":"1.0"},"canonical_sha256":"363dc20be52127732a83694d46549a6db732ea97ee4b1194f03723574bccd5be","source":{"kind":"arxiv","id":"1809.08453","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08453","created_at":"2026-05-18T00:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08453v1","created_at":"2026-05-18T00:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08453","created_at":"2026-05-18T00:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"GY64EC7FEETX","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GY64EC7FEETXGKUD","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GY64EC7F","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GY64EC7FEETXGKUDNFGUMVE2NW","target":"record","payload":{"canonical_record":{"source":{"id":"1809.08453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-09-22T16:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"10853333f09587d719e1c90d270f1bb5dad8d6cccf832f96505430e2e8513762","abstract_canon_sha256":"6439d2115c29f871cda21009ca2d07cc143802cefd0cd472350e6a30bba81263"},"schema_version":"1.0"},"canonical_sha256":"363dc20be52127732a83694d46549a6db732ea97ee4b1194f03723574bccd5be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:08.405742Z","signature_b64":"+ywCmZVLM6HjT2ZTxnONoD2fmQpSfRN+ZlWeW2bib4iftOv6hMILHAu4JpMnb+xu1E97Tlf2sHUHP95XMif2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"363dc20be52127732a83694d46549a6db732ea97ee4b1194f03723574bccd5be","last_reissued_at":"2026-05-18T00:05:08.404990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:08.404990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.08453","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ezyy7NVM5ySoeNPaxrCwn5tgjwdOL3PARpyNW9sPGUbbcSD0QIjxxmR3rPAaCRiFhxNhSfz2V2WL1Jt/DsqeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:29:51.702142Z"},"content_sha256":"5c7a34b1c06c8d2c7e3c59db06e3da0e1c3f3bcc215645b905048cd762decc01","schema_version":"1.0","event_id":"sha256:5c7a34b1c06c8d2c7e3c59db06e3da0e1c3f3bcc215645b905048cd762decc01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GY64EC7FEETXGKUDNFGUMVE2NW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimizing a Generalized Gini Index in Stable Marriage Problems: NP-Hardness, Approximation and a Polynomial Time Special Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Hugo Gilbert, Olivier Spanjaard","submitted_at":"2018-09-22T16:39:08Z","abstract_excerpt":"This paper deals with fairness in stable marriage problems. The idea studied here is to achieve fairness thanks to a Generalized Gini Index (GGI), a well-known criterion in inequality measurement, that includes both the egalitarian and utilitarian criteria as special cases. We show that determining a stable marriage optimizing a GGI criterion of agents' disutilities is an NP-hard problem. We then provide a polynomial time 2-approximation algorithm in the general case, as well as an exact algorithm which is polynomial time in the case of a constant number of non-zero weights parametrizing the G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08453","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fBOk3LtsT6iwhnlq4pqsaXwpj3/6LtX4yFEGykjHR+8fs1iiWJQagbqoOcrf+6C6qJHcF+QnGfHpM48rJJzkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:29:51.702490Z"},"content_sha256":"6251100aed30b433b4c212845a0a3f4ba20555df3726a97f0bca0c34c664cc74","schema_version":"1.0","event_id":"sha256:6251100aed30b433b4c212845a0a3f4ba20555df3726a97f0bca0c34c664cc74"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GY64EC7FEETXGKUDNFGUMVE2NW/bundle.json","state_url":"https://pith.science/pith/GY64EC7FEETXGKUDNFGUMVE2NW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GY64EC7FEETXGKUDNFGUMVE2NW/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":"2026-06-27T08:29:51Z","links":{"resolver":"https://pith.science/pith/GY64EC7FEETXGKUDNFGUMVE2NW","bundle":"https://pith.science/pith/GY64EC7FEETXGKUDNFGUMVE2NW/bundle.json","state":"https://pith.science/pith/GY64EC7FEETXGKUDNFGUMVE2NW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GY64EC7FEETXGKUDNFGUMVE2NW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GY64EC7FEETXGKUDNFGUMVE2NW","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":"6439d2115c29f871cda21009ca2d07cc143802cefd0cd472350e6a30bba81263","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-09-22T16:39:08Z","title_canon_sha256":"10853333f09587d719e1c90d270f1bb5dad8d6cccf832f96505430e2e8513762"},"schema_version":"1.0","source":{"id":"1809.08453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.08453","created_at":"2026-05-18T00:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"1809.08453v1","created_at":"2026-05-18T00:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.08453","created_at":"2026-05-18T00:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"GY64EC7FEETX","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GY64EC7FEETXGKUD","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GY64EC7F","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:6251100aed30b433b4c212845a0a3f4ba20555df3726a97f0bca0c34c664cc74","target":"graph","created_at":"2026-05-18T00:05:08Z","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":"This paper deals with fairness in stable marriage problems. The idea studied here is to achieve fairness thanks to a Generalized Gini Index (GGI), a well-known criterion in inequality measurement, that includes both the egalitarian and utilitarian criteria as special cases. We show that determining a stable marriage optimizing a GGI criterion of agents' disutilities is an NP-hard problem. We then provide a polynomial time 2-approximation algorithm in the general case, as well as an exact algorithm which is polynomial time in the case of a constant number of non-zero weights parametrizing the G","authors_text":"Hugo Gilbert, Olivier Spanjaard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-09-22T16:39:08Z","title":"Optimizing a Generalized Gini Index in Stable Marriage Problems: NP-Hardness, Approximation and a Polynomial Time Special Case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08453","kind":"arxiv","version":1},"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":"sha256:5c7a34b1c06c8d2c7e3c59db06e3da0e1c3f3bcc215645b905048cd762decc01","target":"record","created_at":"2026-05-18T00:05:08Z","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":"6439d2115c29f871cda21009ca2d07cc143802cefd0cd472350e6a30bba81263","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-09-22T16:39:08Z","title_canon_sha256":"10853333f09587d719e1c90d270f1bb5dad8d6cccf832f96505430e2e8513762"},"schema_version":"1.0","source":{"id":"1809.08453","kind":"arxiv","version":1}},"canonical_sha256":"363dc20be52127732a83694d46549a6db732ea97ee4b1194f03723574bccd5be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"363dc20be52127732a83694d46549a6db732ea97ee4b1194f03723574bccd5be","first_computed_at":"2026-05-18T00:05:08.404990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:08.404990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+ywCmZVLM6HjT2ZTxnONoD2fmQpSfRN+ZlWeW2bib4iftOv6hMILHAu4JpMnb+xu1E97Tlf2sHUHP95XMif2Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:08.405742Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.08453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c7a34b1c06c8d2c7e3c59db06e3da0e1c3f3bcc215645b905048cd762decc01","sha256:6251100aed30b433b4c212845a0a3f4ba20555df3726a97f0bca0c34c664cc74"],"state_sha256":"46b70e0c181de1b9cc1957ab726042ebc1528e1f4ebaf02221461a48bf6178c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0VsQFSzqw/6xg3f+5VCrc40kldfgpZ9bO83fQNrznOdKsswhKIw+QDSCrWIAP+WRXAJk2RamJfnJerRsd11pCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T08:29:51.704390Z","bundle_sha256":"69dd6165c4cfd808447f607656237fa861b651b22e9fef9b04f77c82c0601ac0"}}