{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FG3JLFEXY3HE4BEW2RDNUBIOCM","short_pith_number":"pith:FG3JLFEX","schema_version":"1.0","canonical_sha256":"29b6959497c6ce4e0496d446da050e133369f4e76aae667109cd1a1d07bb4cb8","source":{"kind":"arxiv","id":"1501.00563","version":2},"attestation_state":"computed","paper":{"title":"Spotting Trees with Few Leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andreas Bj\\\"orklund, {\\L}ukasz Kowalik, Meirav Zehavi, Vikram Kamat","submitted_at":"2015-01-03T13:19:12Z","abstract_excerpt":"We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\\\"orklund [FOCS'10], and Bj\\\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some $k$-vertex tree with $l$ leaves in an $n$-vertex undirected graph in $O^*(1.657^k2^{l/2})$ time. It can be applied as a subroutine to solve the $k$-Internal Spanning Tree ($k$-IST) problem in $O^*(\\min(3.455^k, 1.946^n))$ time using polynomial space, improving upon previous algorithms for this problem. In particular, for the first time we break the natural barr"},"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":"1501.00563","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-01-03T13:19:12Z","cross_cats_sorted":[],"title_canon_sha256":"f1730b6a7c83c056f4351a0b9bc5ddf1063a6da7b62ffc8c03af24ba87c26321","abstract_canon_sha256":"9bc8a12e4f5148fbb1bc7e9eae6138582d641b69a7a23f1a71381d392cd8a664"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:38.417429Z","signature_b64":"tLpaAgLGzQtjVqE1ckTRABrEFsWNHzNSxbK4NVX7mrcA8GaJsHrufUfad+EjoYSBb7upTEf9D5zViLn0EopCAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29b6959497c6ce4e0496d446da050e133369f4e76aae667109cd1a1d07bb4cb8","last_reissued_at":"2026-05-18T02:26:38.416905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:38.416905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spotting Trees with Few Leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andreas Bj\\\"orklund, {\\L}ukasz Kowalik, Meirav Zehavi, Vikram Kamat","submitted_at":"2015-01-03T13:19:12Z","abstract_excerpt":"We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\\\"orklund [FOCS'10], and Bj\\\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some $k$-vertex tree with $l$ leaves in an $n$-vertex undirected graph in $O^*(1.657^k2^{l/2})$ time. It can be applied as a subroutine to solve the $k$-Internal Spanning Tree ($k$-IST) problem in $O^*(\\min(3.455^k, 1.946^n))$ time using polynomial space, improving upon previous algorithms for this problem. In particular, for the first time we break the natural barr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00563","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":"1501.00563","created_at":"2026-05-18T02:26:38.416990+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00563v2","created_at":"2026-05-18T02:26:38.416990+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00563","created_at":"2026-05-18T02:26:38.416990+00:00"},{"alias_kind":"pith_short_12","alias_value":"FG3JLFEXY3HE","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FG3JLFEXY3HE4BEW","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FG3JLFEX","created_at":"2026-05-18T12:29:19.899920+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/FG3JLFEXY3HE4BEW2RDNUBIOCM","json":"https://pith.science/pith/FG3JLFEXY3HE4BEW2RDNUBIOCM.json","graph_json":"https://pith.science/api/pith-number/FG3JLFEXY3HE4BEW2RDNUBIOCM/graph.json","events_json":"https://pith.science/api/pith-number/FG3JLFEXY3HE4BEW2RDNUBIOCM/events.json","paper":"https://pith.science/paper/FG3JLFEX"},"agent_actions":{"view_html":"https://pith.science/pith/FG3JLFEXY3HE4BEW2RDNUBIOCM","download_json":"https://pith.science/pith/FG3JLFEXY3HE4BEW2RDNUBIOCM.json","view_paper":"https://pith.science/paper/FG3JLFEX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00563&json=true","fetch_graph":"https://pith.science/api/pith-number/FG3JLFEXY3HE4BEW2RDNUBIOCM/graph.json","fetch_events":"https://pith.science/api/pith-number/FG3JLFEXY3HE4BEW2RDNUBIOCM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FG3JLFEXY3HE4BEW2RDNUBIOCM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FG3JLFEXY3HE4BEW2RDNUBIOCM/action/storage_attestation","attest_author":"https://pith.science/pith/FG3JLFEXY3HE4BEW2RDNUBIOCM/action/author_attestation","sign_citation":"https://pith.science/pith/FG3JLFEXY3HE4BEW2RDNUBIOCM/action/citation_signature","submit_replication":"https://pith.science/pith/FG3JLFEXY3HE4BEW2RDNUBIOCM/action/replication_record"}},"created_at":"2026-05-18T02:26:38.416990+00:00","updated_at":"2026-05-18T02:26:38.416990+00:00"}