{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:DFDH3HQYQWCKGLNS3QKXUEFHQ6","short_pith_number":"pith:DFDH3HQY","schema_version":"1.0","canonical_sha256":"19467d9e188584a32db2dc157a10a787b5f545f37a1b389a94848e3932e88aa2","source":{"kind":"arxiv","id":"2603.23193","version":3},"attestation_state":"computed","paper":{"title":"Algorithms and Hardness for Geodetic Set on Tree-like Digraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Geodetic Set can be solved in polynomial time on ditrees.","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Florent Foucaud, Lucas Lorieau, Morteza Mohammad-Noori, Narges Ghareghani, Prafullkumar Tale, Rasa Parvini Oskuei","submitted_at":"2026-03-24T13:41:12Z","abstract_excerpt":"In the GEODETIC SET problem, an input is a (di)graph $G$ and integer $k$, and the objective is to decide whether there exists a vertex subset $S$ of size $k$ such that any vertex in $V(G)\\setminus S$ lies on a shortest (directed) path between two vertices in $S$. The problem has been studied on undirected and directed graphs from both algorithmic and graph-theoretical perspectives.\n  We focus on directed graphs and prove that GEODETIC SET admits a polynomial-time algorithm on ditrees, that is, digraphs with possible 2-cycles when the underlying undirected graph is a tree (after deleting possib"},"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":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2603.23193","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-03-24T13:41:12Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"b3b77f6c3fcb69c7a27b2be5ca96099fa47725fdbdfc8356995ebcb1bbe416fc","abstract_canon_sha256":"ab5c1e2e6bc99cb4381e893c438d9c0f7bb7acb297a1d45bf250987bfa93566d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:30.748039Z","signature_b64":"Rl9zFb/I42yEcUFFNlr/BpOOwZ+eBUxdcIRcWCshR1zL74HAEh6D1AlNikVdKtXsPdXhIdVbuG/Bk2gliohqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19467d9e188584a32db2dc157a10a787b5f545f37a1b389a94848e3932e88aa2","last_reissued_at":"2026-05-18T02:44:30.747517Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:30.747517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algorithms and Hardness for Geodetic Set on Tree-like Digraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Geodetic Set can be solved in polynomial time on ditrees.","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Florent Foucaud, Lucas Lorieau, Morteza Mohammad-Noori, Narges Ghareghani, Prafullkumar Tale, Rasa Parvini Oskuei","submitted_at":"2026-03-24T13:41:12Z","abstract_excerpt":"In the GEODETIC SET problem, an input is a (di)graph $G$ and integer $k$, and the objective is to decide whether there exists a vertex subset $S$ of size $k$ such that any vertex in $V(G)\\setminus S$ lies on a shortest (directed) path between two vertices in $S$. The problem has been studied on undirected and directed graphs from both algorithmic and graph-theoretical perspectives.\n  We focus on directed graphs and prove that GEODETIC SET admits a polynomial-time algorithm on ditrees, that is, digraphs with possible 2-cycles when the underlying undirected graph is a tree (after deleting possib"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"GEODETIC SET admits a polynomial-time algorithm on ditrees, that is, digraphs with possible 2-cycles when the underlying undirected graph is a tree (after deleting possible parallel edges).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The input digraphs satisfy the structural properties like being ditrees or having bounded feedback edge set, and the algorithms correctly compute shortest paths in these structures without hidden exponential factors.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Geodetic Set can be solved in polynomial time on ditrees and in FPT time parameterized by feedback edge set on 2-cycle-free digraphs, but is NP-hard on DAGs with constant feedback vertex set and pathwidth.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Geodetic Set can be solved in polynomial time on ditrees.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5cc06fc7d4d2da81bb5ef206267ce150d6289f7f75da696193fdb688528a28f6"},"source":{"id":"2603.23193","kind":"arxiv","version":3},"verdict":{"id":"f56fdb80-258a-456b-be7b-d1a32ec9d634","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T00:24:52.706814Z","strongest_claim":"GEODETIC SET admits a polynomial-time algorithm on ditrees, that is, digraphs with possible 2-cycles when the underlying undirected graph is a tree (after deleting possible parallel edges).","one_line_summary":"Geodetic Set can be solved in polynomial time on ditrees and in FPT time parameterized by feedback edge set on 2-cycle-free digraphs, but is NP-hard on DAGs with constant feedback vertex set and pathwidth.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The input digraphs satisfy the structural properties like being ditrees or having bounded feedback edge set, and the algorithms correctly compute shortest paths in these structures without hidden exponential factors.","pith_extraction_headline":"Geodetic Set can be solved in polynomial time on ditrees."},"references":{"count":30,"sample":[{"doi":"","year":2022,"title":"Discrete Mathematics345(10), 112985 (2022)","work_id":"a9367b3e-a2e0-468f-bd1c-68f613ddfb87","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Discrete Applied Mathematics323, 14–27 (2022)","work_id":"187e2e69-3f7d-4ec3-b488-bf1769e5d305","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Bergougnoux, B., Defrain, O., Mc Inerney, F.: Enumerating minimal solution sets for metric graph problems. In: Proc. of the 50th Inter- national Workshop on Graph-Theoretic Concepts in Computer Scienc","work_id":"5c54454e-9823-4a4d-a11b-683b381411b7","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"In: 31st International Symposium on Algorithms and Compu- tation (ISAAC 2020)","work_id":"6d663b8a-da07-4700-9b8d-4964158c0890","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"In: Proceedings of the 6th International Conference on Algo- rithms and Discrete Applied Mathematics (CALDAM 2020)","work_id":"be4b2222-2b52-4958-89d9-24d68ab6d767","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":30,"snapshot_sha256":"6ae957cbb80e737bba18a0b09e12ebe53beb2dfaf284d2b1ba2c689ebe5bf957","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":"2603.23193","created_at":"2026-05-18T02:44:30.747587+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.23193v3","created_at":"2026-05-18T02:44:30.747587+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.23193","created_at":"2026-05-18T02:44:30.747587+00:00"},{"alias_kind":"pith_short_12","alias_value":"DFDH3HQYQWCK","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"DFDH3HQYQWCKGLNS","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"DFDH3HQY","created_at":"2026-05-18T12:33:37.589309+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/DFDH3HQYQWCKGLNS3QKXUEFHQ6","json":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6.json","graph_json":"https://pith.science/api/pith-number/DFDH3HQYQWCKGLNS3QKXUEFHQ6/graph.json","events_json":"https://pith.science/api/pith-number/DFDH3HQYQWCKGLNS3QKXUEFHQ6/events.json","paper":"https://pith.science/paper/DFDH3HQY"},"agent_actions":{"view_html":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6","download_json":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6.json","view_paper":"https://pith.science/paper/DFDH3HQY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.23193&json=true","fetch_graph":"https://pith.science/api/pith-number/DFDH3HQYQWCKGLNS3QKXUEFHQ6/graph.json","fetch_events":"https://pith.science/api/pith-number/DFDH3HQYQWCKGLNS3QKXUEFHQ6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6/action/storage_attestation","attest_author":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6/action/author_attestation","sign_citation":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6/action/citation_signature","submit_replication":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6/action/replication_record"}},"created_at":"2026-05-18T02:44:30.747587+00:00","updated_at":"2026-05-18T02:44:30.747587+00:00"}