{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:4LT2TVC7NAL3AOPYNJ4T77FDQX","short_pith_number":"pith:4LT2TVC7","schema_version":"1.0","canonical_sha256":"e2e7a9d45f6817b039f86a793ffca385d284384266ca47b69329d10d0cefd0e8","source":{"kind":"arxiv","id":"1910.12848","version":1},"attestation_state":"computed","paper":{"title":"Bounded Degree Group Steiner Tree Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Guy Kortsarz, Zeev Nutov","submitted_at":"2019-10-28T17:55:16Z","abstract_excerpt":"We study two problems that seek a subtree $T$ of a graph $G=(V,E)$ such that $T$ satisfies a certain property and has minimal maximum degree.\n  - In the Min-Degree Group Steiner Tree problem we are given a collection ${\\cal S}$ of groups (subsets of $V$) and $T$ should contain a node from every group.\n  - In the Min-Degree Steiner $k$-Tree problem we are given a set $R$ of terminals and an integer $k$, and $T$ should contain at least $k$ terminals.\n  We show that if the former problem admits approximation ratio $\\rho$ then the later problem admits approximation ratio $\\rho \\cdot O(\\log k)$. Fo"},"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":"1910.12848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-10-28T17:55:16Z","cross_cats_sorted":[],"title_canon_sha256":"63af63167c87ff2d03bcecd1638d1a0b4c9dd00e1ed0039c8df2138bb50b583b","abstract_canon_sha256":"ea69ea1de40194739f6f31378f2316d20a6264e496f105e60b4fc6250ca85738"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:15:20.512565Z","signature_b64":"I4WZtiRhJVt0ZTg8NZGmPAaYpJOYDFihAguYzLP68o/Tw+3mV0HbJSC/B3b2CZle3Eqb8CWgep+jz1pgLiw6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2e7a9d45f6817b039f86a793ffca385d284384266ca47b69329d10d0cefd0e8","last_reissued_at":"2026-07-05T00:15:20.512123Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:15:20.512123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded Degree Group Steiner Tree Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Guy Kortsarz, Zeev Nutov","submitted_at":"2019-10-28T17:55:16Z","abstract_excerpt":"We study two problems that seek a subtree $T$ of a graph $G=(V,E)$ such that $T$ satisfies a certain property and has minimal maximum degree.\n  - In the Min-Degree Group Steiner Tree problem we are given a collection ${\\cal S}$ of groups (subsets of $V$) and $T$ should contain a node from every group.\n  - In the Min-Degree Steiner $k$-Tree problem we are given a set $R$ of terminals and an integer $k$, and $T$ should contain at least $k$ terminals.\n  We show that if the former problem admits approximation ratio $\\rho$ then the later problem admits approximation ratio $\\rho \\cdot O(\\log k)$. Fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.12848","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/1910.12848/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":"1910.12848","created_at":"2026-07-05T00:15:20.512183+00:00"},{"alias_kind":"arxiv_version","alias_value":"1910.12848v1","created_at":"2026-07-05T00:15:20.512183+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.12848","created_at":"2026-07-05T00:15:20.512183+00:00"},{"alias_kind":"pith_short_12","alias_value":"4LT2TVC7NAL3","created_at":"2026-07-05T00:15:20.512183+00:00"},{"alias_kind":"pith_short_16","alias_value":"4LT2TVC7NAL3AOPY","created_at":"2026-07-05T00:15:20.512183+00:00"},{"alias_kind":"pith_short_8","alias_value":"4LT2TVC7","created_at":"2026-07-05T00:15:20.512183+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/4LT2TVC7NAL3AOPYNJ4T77FDQX","json":"https://pith.science/pith/4LT2TVC7NAL3AOPYNJ4T77FDQX.json","graph_json":"https://pith.science/api/pith-number/4LT2TVC7NAL3AOPYNJ4T77FDQX/graph.json","events_json":"https://pith.science/api/pith-number/4LT2TVC7NAL3AOPYNJ4T77FDQX/events.json","paper":"https://pith.science/paper/4LT2TVC7"},"agent_actions":{"view_html":"https://pith.science/pith/4LT2TVC7NAL3AOPYNJ4T77FDQX","download_json":"https://pith.science/pith/4LT2TVC7NAL3AOPYNJ4T77FDQX.json","view_paper":"https://pith.science/paper/4LT2TVC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1910.12848&json=true","fetch_graph":"https://pith.science/api/pith-number/4LT2TVC7NAL3AOPYNJ4T77FDQX/graph.json","fetch_events":"https://pith.science/api/pith-number/4LT2TVC7NAL3AOPYNJ4T77FDQX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4LT2TVC7NAL3AOPYNJ4T77FDQX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4LT2TVC7NAL3AOPYNJ4T77FDQX/action/storage_attestation","attest_author":"https://pith.science/pith/4LT2TVC7NAL3AOPYNJ4T77FDQX/action/author_attestation","sign_citation":"https://pith.science/pith/4LT2TVC7NAL3AOPYNJ4T77FDQX/action/citation_signature","submit_replication":"https://pith.science/pith/4LT2TVC7NAL3AOPYNJ4T77FDQX/action/replication_record"}},"created_at":"2026-07-05T00:15:20.512183+00:00","updated_at":"2026-07-05T00:15:20.512183+00:00"}