{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:2OSJUG5OUR4RWCDVQBEAX2OKD6","short_pith_number":"pith:2OSJUG5O","schema_version":"1.0","canonical_sha256":"d3a49a1baea4791b087580480be9ca1fa75712d6e097987dab5ac2f196c14e8d","source":{"kind":"arxiv","id":"2112.06188","version":1},"attestation_state":"computed","paper":{"title":"Parallel Batch-Dynamic $k$d-Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DB"],"primary_cat":"cs.DS","authors_text":"Julian Shun (1) ((1) MIT CSAIL), Laxman Dhulipala (1), Rahul Yesantharao (1), Yiqiu Wang (1)","submitted_at":"2021-12-12T09:08:41Z","abstract_excerpt":"$k$d-trees are widely used in parallel databases to support efficient neighborhood/similarity queries. Supporting parallel updates to $k$d-trees is therefore an important operation. In this paper, we present BDL-tree, a parallel, batch-dynamic implementation of a $k$d-tree that allows for efficient parallel $k$-NN queries over dynamically changing point sets. BDL-trees consist of a log-structured set of $k$d-trees which can be used to efficiently insert or delete batches of points in parallel with polylogarithmic depth. Specifically, given a BDL-tree with $n$ points, each batch of $B$ updates "},"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":"2112.06188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-12-12T09:08:41Z","cross_cats_sorted":["cs.DB"],"title_canon_sha256":"55711a92478c574099bcada95888b3c97c1ff1d1f7a1039a25b292002473fb7b","abstract_canon_sha256":"4a357ecae3d0a65d30b87eebba2eaa53c2f0f65cc93e36b3b492b11fa92a75b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:40:11.217542Z","signature_b64":"KWWsd3kcm7vDRglr91WiNkBai4OFycxqUOUengwkM+Abi3qoajFCEtPasXFoPmx5bgReL6tLEIPiGfly9ebQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3a49a1baea4791b087580480be9ca1fa75712d6e097987dab5ac2f196c14e8d","last_reissued_at":"2026-07-05T03:40:11.217084Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:40:11.217084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parallel Batch-Dynamic $k$d-Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DB"],"primary_cat":"cs.DS","authors_text":"Julian Shun (1) ((1) MIT CSAIL), Laxman Dhulipala (1), Rahul Yesantharao (1), Yiqiu Wang (1)","submitted_at":"2021-12-12T09:08:41Z","abstract_excerpt":"$k$d-trees are widely used in parallel databases to support efficient neighborhood/similarity queries. Supporting parallel updates to $k$d-trees is therefore an important operation. In this paper, we present BDL-tree, a parallel, batch-dynamic implementation of a $k$d-tree that allows for efficient parallel $k$-NN queries over dynamically changing point sets. BDL-trees consist of a log-structured set of $k$d-trees which can be used to efficiently insert or delete batches of points in parallel with polylogarithmic depth. Specifically, given a BDL-tree with $n$ points, each batch of $B$ updates "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.06188","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.06188/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":"2112.06188","created_at":"2026-07-05T03:40:11.217141+00:00"},{"alias_kind":"arxiv_version","alias_value":"2112.06188v1","created_at":"2026-07-05T03:40:11.217141+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.06188","created_at":"2026-07-05T03:40:11.217141+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OSJUG5OUR4R","created_at":"2026-07-05T03:40:11.217141+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OSJUG5OUR4RWCDV","created_at":"2026-07-05T03:40:11.217141+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OSJUG5O","created_at":"2026-07-05T03:40:11.217141+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.03640","citing_title":"In-memory Multidimensional Indexing Using the skd-tree","ref_index":89,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2OSJUG5OUR4RWCDVQBEAX2OKD6","json":"https://pith.science/pith/2OSJUG5OUR4RWCDVQBEAX2OKD6.json","graph_json":"https://pith.science/api/pith-number/2OSJUG5OUR4RWCDVQBEAX2OKD6/graph.json","events_json":"https://pith.science/api/pith-number/2OSJUG5OUR4RWCDVQBEAX2OKD6/events.json","paper":"https://pith.science/paper/2OSJUG5O"},"agent_actions":{"view_html":"https://pith.science/pith/2OSJUG5OUR4RWCDVQBEAX2OKD6","download_json":"https://pith.science/pith/2OSJUG5OUR4RWCDVQBEAX2OKD6.json","view_paper":"https://pith.science/paper/2OSJUG5O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2112.06188&json=true","fetch_graph":"https://pith.science/api/pith-number/2OSJUG5OUR4RWCDVQBEAX2OKD6/graph.json","fetch_events":"https://pith.science/api/pith-number/2OSJUG5OUR4RWCDVQBEAX2OKD6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OSJUG5OUR4RWCDVQBEAX2OKD6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OSJUG5OUR4RWCDVQBEAX2OKD6/action/storage_attestation","attest_author":"https://pith.science/pith/2OSJUG5OUR4RWCDVQBEAX2OKD6/action/author_attestation","sign_citation":"https://pith.science/pith/2OSJUG5OUR4RWCDVQBEAX2OKD6/action/citation_signature","submit_replication":"https://pith.science/pith/2OSJUG5OUR4RWCDVQBEAX2OKD6/action/replication_record"}},"created_at":"2026-07-05T03:40:11.217141+00:00","updated_at":"2026-07-05T03:40:11.217141+00:00"}