{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YZ2EOIJ4Q47BPXZ2KAXHV6DXIO","short_pith_number":"pith:YZ2EOIJ4","schema_version":"1.0","canonical_sha256":"c67447213c873e17df3a502e7af87743b617ebce35f680f37fd89b0c2187e9d6","source":{"kind":"arxiv","id":"1304.3653","version":1},"attestation_state":"computed","paper":{"title":"Algorithms for Cut Problems on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Binhai Zhu, Boting Yang, Fenghui Zhang, Ge Xia, Guohui Lin, Iyad Kanj, Jinhui Xu, Peng Zhang, Tian Liu, Weitian Tong","submitted_at":"2013-04-12T14:57:47Z","abstract_excerpt":"We study the {\\sc multicut on trees} and the {\\sc generalized multiway Cut on trees} problems. For the {\\sc multicut on trees} problem, we present a parameterized algorithm that runs in time $O^{*}(\\rho^k)$, where $\\rho = \\sqrt{\\sqrt{2} + 1} \\approx 1.555$ is the positive root of the polynomial $x^4-2x^2-1$. This improves the current-best algorithm of Chen et al. that runs in time $O^{*}(1.619^k)$. For the {\\sc generalized multiway cut on trees} problem, we show that this problem is solvable in polynomial time if the number of terminal sets is fixed; this answers an open question posed in a re"},"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":"1304.3653","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-04-12T14:57:47Z","cross_cats_sorted":[],"title_canon_sha256":"076248fe4695081bda703a1479e60fa23315b4a036943bf63e05281a8f6bd9fa","abstract_canon_sha256":"d8dfe8e8fbd2c3a2b0196bd628a62316cd19b2363f3fb86aa69f217b5d8cbfab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:06.954687Z","signature_b64":"ZbruKmrTtGy58uQDcxNLntgAwo+/DQKYRR1xufGZ6jgyzXtEOXJM8xSSvwUBBSg1hlBhxczMDaaIB201e1PnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c67447213c873e17df3a502e7af87743b617ebce35f680f37fd89b0c2187e9d6","last_reissued_at":"2026-05-18T03:28:06.953810Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:06.953810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algorithms for Cut Problems on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Binhai Zhu, Boting Yang, Fenghui Zhang, Ge Xia, Guohui Lin, Iyad Kanj, Jinhui Xu, Peng Zhang, Tian Liu, Weitian Tong","submitted_at":"2013-04-12T14:57:47Z","abstract_excerpt":"We study the {\\sc multicut on trees} and the {\\sc generalized multiway Cut on trees} problems. For the {\\sc multicut on trees} problem, we present a parameterized algorithm that runs in time $O^{*}(\\rho^k)$, where $\\rho = \\sqrt{\\sqrt{2} + 1} \\approx 1.555$ is the positive root of the polynomial $x^4-2x^2-1$. This improves the current-best algorithm of Chen et al. that runs in time $O^{*}(1.619^k)$. For the {\\sc generalized multiway cut on trees} problem, we show that this problem is solvable in polynomial time if the number of terminal sets is fixed; this answers an open question posed in a re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3653","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1304.3653","created_at":"2026-05-18T03:28:06.953985+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.3653v1","created_at":"2026-05-18T03:28:06.953985+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3653","created_at":"2026-05-18T03:28:06.953985+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZ2EOIJ4Q47B","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZ2EOIJ4Q47BPXZ2","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZ2EOIJ4","created_at":"2026-05-18T12:28:09.283467+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/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO","json":"https://pith.science/pith/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO.json","graph_json":"https://pith.science/api/pith-number/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO/graph.json","events_json":"https://pith.science/api/pith-number/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO/events.json","paper":"https://pith.science/paper/YZ2EOIJ4"},"agent_actions":{"view_html":"https://pith.science/pith/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO","download_json":"https://pith.science/pith/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO.json","view_paper":"https://pith.science/paper/YZ2EOIJ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.3653&json=true","fetch_graph":"https://pith.science/api/pith-number/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO/graph.json","fetch_events":"https://pith.science/api/pith-number/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO/action/storage_attestation","attest_author":"https://pith.science/pith/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO/action/author_attestation","sign_citation":"https://pith.science/pith/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO/action/citation_signature","submit_replication":"https://pith.science/pith/YZ2EOIJ4Q47BPXZ2KAXHV6DXIO/action/replication_record"}},"created_at":"2026-05-18T03:28:06.953985+00:00","updated_at":"2026-05-18T03:28:06.953985+00:00"}