{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:2ZEK44KU67BP3IIZSZBOZL6O4P","short_pith_number":"pith:2ZEK44KU","schema_version":"1.0","canonical_sha256":"d648ae7154f7c2fda1199642ecafcee3de6086b9a1c0626b4ab9df6a45ab43ac","source":{"kind":"arxiv","id":"2002.01258","version":2},"attestation_state":"computed","paper":{"title":"From tree matching to sparse graph alignment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.DS","authors_text":"Laurent Massouli\\'e, Luca Ganassali","submitted_at":"2020-02-04T12:36:21Z","abstract_excerpt":"In this paper we consider alignment of sparse graphs, for which we introduce the Neighborhood Tree Matching Algorithm (NTMA). For correlated Erd\\H{o}s-R\\'{e}nyi random graphs, we prove that the algorithm returns -- in polynomial time -- a positive fraction of correctly matched vertices, and a vanishing fraction of mismatches. This result holds with average degree of the graphs in $O(1)$ and correlation parameter $s$ that can be bounded away from 1, conditions under which random graph alignment is particularly challenging. As a byproduct of the analysis we introduce a matching metric between tr"},"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":"2002.01258","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-02-04T12:36:21Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e3ee4bcda3e655f45f9ae97f6d129ff405b58bd132b6f878fcb4a57ad7a63407","abstract_canon_sha256":"16dbdd9130897ceecb57e94393ae8a3e3d32bfa9efddcea60fc04209df832abe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:47:42.876065Z","signature_b64":"P5yHEIDTwoM3Yj6e1cuqsUK1loievho1HZwKd4ERNRs1Vd8DWYgj9GmBEoL7Mqe43TNrXZzwlxLHKnRiiZ2LAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d648ae7154f7c2fda1199642ecafcee3de6086b9a1c0626b4ab9df6a45ab43ac","last_reissued_at":"2026-07-05T01:47:42.875621Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:47:42.875621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From tree matching to sparse graph alignment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.DS","authors_text":"Laurent Massouli\\'e, Luca Ganassali","submitted_at":"2020-02-04T12:36:21Z","abstract_excerpt":"In this paper we consider alignment of sparse graphs, for which we introduce the Neighborhood Tree Matching Algorithm (NTMA). For correlated Erd\\H{o}s-R\\'{e}nyi random graphs, we prove that the algorithm returns -- in polynomial time -- a positive fraction of correctly matched vertices, and a vanishing fraction of mismatches. This result holds with average degree of the graphs in $O(1)$ and correlation parameter $s$ that can be bounded away from 1, conditions under which random graph alignment is particularly challenging. As a byproduct of the analysis we introduce a matching metric between tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.01258","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/2002.01258/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2002.01258","created_at":"2026-07-05T01:47:42.875679+00:00"},{"alias_kind":"arxiv_version","alias_value":"2002.01258v2","created_at":"2026-07-05T01:47:42.875679+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.01258","created_at":"2026-07-05T01:47:42.875679+00:00"},{"alias_kind":"pith_short_12","alias_value":"2ZEK44KU67BP","created_at":"2026-07-05T01:47:42.875679+00:00"},{"alias_kind":"pith_short_16","alias_value":"2ZEK44KU67BP3IIZ","created_at":"2026-07-05T01:47:42.875679+00:00"},{"alias_kind":"pith_short_8","alias_value":"2ZEK44KU","created_at":"2026-07-05T01:47:42.875679+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.08538","citing_title":"High-Dimensional Procrustes Matching via Tree Counts","ref_index":19,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2ZEK44KU67BP3IIZSZBOZL6O4P","json":"https://pith.science/pith/2ZEK44KU67BP3IIZSZBOZL6O4P.json","graph_json":"https://pith.science/api/pith-number/2ZEK44KU67BP3IIZSZBOZL6O4P/graph.json","events_json":"https://pith.science/api/pith-number/2ZEK44KU67BP3IIZSZBOZL6O4P/events.json","paper":"https://pith.science/paper/2ZEK44KU"},"agent_actions":{"view_html":"https://pith.science/pith/2ZEK44KU67BP3IIZSZBOZL6O4P","download_json":"https://pith.science/pith/2ZEK44KU67BP3IIZSZBOZL6O4P.json","view_paper":"https://pith.science/paper/2ZEK44KU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2002.01258&json=true","fetch_graph":"https://pith.science/api/pith-number/2ZEK44KU67BP3IIZSZBOZL6O4P/graph.json","fetch_events":"https://pith.science/api/pith-number/2ZEK44KU67BP3IIZSZBOZL6O4P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2ZEK44KU67BP3IIZSZBOZL6O4P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2ZEK44KU67BP3IIZSZBOZL6O4P/action/storage_attestation","attest_author":"https://pith.science/pith/2ZEK44KU67BP3IIZSZBOZL6O4P/action/author_attestation","sign_citation":"https://pith.science/pith/2ZEK44KU67BP3IIZSZBOZL6O4P/action/citation_signature","submit_replication":"https://pith.science/pith/2ZEK44KU67BP3IIZSZBOZL6O4P/action/replication_record"}},"created_at":"2026-07-05T01:47:42.875679+00:00","updated_at":"2026-07-05T01:47:42.875679+00:00"}