{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6VCYIJED5SDEUYR4IZDQV55VFO","short_pith_number":"pith:6VCYIJED","schema_version":"1.0","canonical_sha256":"f545842483ec864a623c46470af7b52b8f96adceace30345cef9aef645ec5f06","source":{"kind":"arxiv","id":"1512.08147","version":2},"attestation_state":"computed","paper":{"title":"Sublinear-Time Maintenance of Breadth-First Spanning Trees in Partially Dynamic Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Danupon Nanongkai, Monika Henzinger, Sebastian Krinninger","submitted_at":"2015-12-26T21:54:27Z","abstract_excerpt":"We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic $(1+\\epsilon)$-approximation algorithms whose amortized time (over some number of link changes) is sublinear in $D$, the maximum diameter of the network.\n  Our technique also leads to a deterministic $(1+\\epsilon)$-approximate incremental algorithm for single-source shortest paths (SSSP) in the sequential (usual RAM) model. Prior to our work, the state of the art"},"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":"1512.08147","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-26T21:54:27Z","cross_cats_sorted":[],"title_canon_sha256":"c01e8fea84739adea9cad558ef3911ef7823b4dc78f71b010f1317f2e9fee53c","abstract_canon_sha256":"6da56e7dc78b81148f033d4ed6d0b55ac05625a7a485def3648fafec3e020fd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:16.530980Z","signature_b64":"K83/ZGI4vjalbs1VA6S7vkTTO6VjUh7QpQYk2vPm6vVOiJdVcWsy/9APHDi/5aJNV5uOcno7JX+FnPZHzEDODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f545842483ec864a623c46470af7b52b8f96adceace30345cef9aef645ec5f06","last_reissued_at":"2026-05-18T00:22:16.530299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:16.530299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sublinear-Time Maintenance of Breadth-First Spanning Trees in Partially Dynamic Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Danupon Nanongkai, Monika Henzinger, Sebastian Krinninger","submitted_at":"2015-12-26T21:54:27Z","abstract_excerpt":"We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic $(1+\\epsilon)$-approximation algorithms whose amortized time (over some number of link changes) is sublinear in $D$, the maximum diameter of the network.\n  Our technique also leads to a deterministic $(1+\\epsilon)$-approximate incremental algorithm for single-source shortest paths (SSSP) in the sequential (usual RAM) model. Prior to our work, the state of the art"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08147","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":""},"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":"1512.08147","created_at":"2026-05-18T00:22:16.530421+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.08147v2","created_at":"2026-05-18T00:22:16.530421+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08147","created_at":"2026-05-18T00:22:16.530421+00:00"},{"alias_kind":"pith_short_12","alias_value":"6VCYIJED5SDE","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6VCYIJED5SDEUYR4","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6VCYIJED","created_at":"2026-05-18T12:29:07.941421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6VCYIJED5SDEUYR4IZDQV55VFO","json":"https://pith.science/pith/6VCYIJED5SDEUYR4IZDQV55VFO.json","graph_json":"https://pith.science/api/pith-number/6VCYIJED5SDEUYR4IZDQV55VFO/graph.json","events_json":"https://pith.science/api/pith-number/6VCYIJED5SDEUYR4IZDQV55VFO/events.json","paper":"https://pith.science/paper/6VCYIJED"},"agent_actions":{"view_html":"https://pith.science/pith/6VCYIJED5SDEUYR4IZDQV55VFO","download_json":"https://pith.science/pith/6VCYIJED5SDEUYR4IZDQV55VFO.json","view_paper":"https://pith.science/paper/6VCYIJED","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.08147&json=true","fetch_graph":"https://pith.science/api/pith-number/6VCYIJED5SDEUYR4IZDQV55VFO/graph.json","fetch_events":"https://pith.science/api/pith-number/6VCYIJED5SDEUYR4IZDQV55VFO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6VCYIJED5SDEUYR4IZDQV55VFO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6VCYIJED5SDEUYR4IZDQV55VFO/action/storage_attestation","attest_author":"https://pith.science/pith/6VCYIJED5SDEUYR4IZDQV55VFO/action/author_attestation","sign_citation":"https://pith.science/pith/6VCYIJED5SDEUYR4IZDQV55VFO/action/citation_signature","submit_replication":"https://pith.science/pith/6VCYIJED5SDEUYR4IZDQV55VFO/action/replication_record"}},"created_at":"2026-05-18T00:22:16.530421+00:00","updated_at":"2026-05-18T00:22:16.530421+00:00"}