{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:FGDK2O7WBRKYJLJAFSUR4DFYHG","short_pith_number":"pith:FGDK2O7W","schema_version":"1.0","canonical_sha256":"2986ad3bf60c5584ad202ca91e0cb839b1daf123094f50398582fa9430bdadcf","source":{"kind":"arxiv","id":"1907.04087","version":1},"attestation_state":"computed","paper":{"title":"PTAS and Exact Algorithms for $r$-Gathering Problems on Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Soh Kumabe, Takanori Maehara","submitted_at":"2019-07-09T11:29:43Z","abstract_excerpt":"r-gathering problem is a variant of facility location problems. In this problem, we are given a set of users and a set of facilities on same metric space. We open some of the facilities and assign each user to an open facility, so that at least r users are assigned to every open facility. We aim to minimize the maximum distance between user and assigned facility. In general, this problem is NP-hard and admit an approximation algorithm with factor 3. It is known that the problem does not admit any approximation algorithm within a factor less than 3. In our another paper, we proved that this pro"},"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":"1907.04087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-09T11:29:43Z","cross_cats_sorted":[],"title_canon_sha256":"bb07eac7e4aac570dfada4c46b3b8f30651d0f7bbdb5eaaf8b2e17a22c2558bd","abstract_canon_sha256":"522e464861c2e631e4a0862e9cf819b2ca193617291d7bee83c8ff522230fee9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:05.727737Z","signature_b64":"r/FLYz79gaxzobtQ++S1wSHby+16AIt4xyxaTMItOgjRrxMCHTzwfSVfSemeQoRTtmhw1evb+xynkO64/nZKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2986ad3bf60c5584ad202ca91e0cb839b1daf123094f50398582fa9430bdadcf","last_reissued_at":"2026-05-17T23:41:05.727074Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:05.727074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"PTAS and Exact Algorithms for $r$-Gathering Problems on Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Soh Kumabe, Takanori Maehara","submitted_at":"2019-07-09T11:29:43Z","abstract_excerpt":"r-gathering problem is a variant of facility location problems. In this problem, we are given a set of users and a set of facilities on same metric space. We open some of the facilities and assign each user to an open facility, so that at least r users are assigned to every open facility. We aim to minimize the maximum distance between user and assigned facility. In general, this problem is NP-hard and admit an approximation algorithm with factor 3. It is known that the problem does not admit any approximation algorithm within a factor less than 3. In our another paper, we proved that this pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04087","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":"1907.04087","created_at":"2026-05-17T23:41:05.727165+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.04087v1","created_at":"2026-05-17T23:41:05.727165+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04087","created_at":"2026-05-17T23:41:05.727165+00:00"},{"alias_kind":"pith_short_12","alias_value":"FGDK2O7WBRKY","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"FGDK2O7WBRKYJLJA","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"FGDK2O7W","created_at":"2026-05-18T12:33:15.570797+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/FGDK2O7WBRKYJLJAFSUR4DFYHG","json":"https://pith.science/pith/FGDK2O7WBRKYJLJAFSUR4DFYHG.json","graph_json":"https://pith.science/api/pith-number/FGDK2O7WBRKYJLJAFSUR4DFYHG/graph.json","events_json":"https://pith.science/api/pith-number/FGDK2O7WBRKYJLJAFSUR4DFYHG/events.json","paper":"https://pith.science/paper/FGDK2O7W"},"agent_actions":{"view_html":"https://pith.science/pith/FGDK2O7WBRKYJLJAFSUR4DFYHG","download_json":"https://pith.science/pith/FGDK2O7WBRKYJLJAFSUR4DFYHG.json","view_paper":"https://pith.science/paper/FGDK2O7W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.04087&json=true","fetch_graph":"https://pith.science/api/pith-number/FGDK2O7WBRKYJLJAFSUR4DFYHG/graph.json","fetch_events":"https://pith.science/api/pith-number/FGDK2O7WBRKYJLJAFSUR4DFYHG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FGDK2O7WBRKYJLJAFSUR4DFYHG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FGDK2O7WBRKYJLJAFSUR4DFYHG/action/storage_attestation","attest_author":"https://pith.science/pith/FGDK2O7WBRKYJLJAFSUR4DFYHG/action/author_attestation","sign_citation":"https://pith.science/pith/FGDK2O7WBRKYJLJAFSUR4DFYHG/action/citation_signature","submit_replication":"https://pith.science/pith/FGDK2O7WBRKYJLJAFSUR4DFYHG/action/replication_record"}},"created_at":"2026-05-17T23:41:05.727165+00:00","updated_at":"2026-05-17T23:41:05.727165+00:00"}