{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2PYPWPGUXFZVTBYCEJQRSNF6NC","short_pith_number":"pith:2PYPWPGU","schema_version":"1.0","canonical_sha256":"d3f0fb3cd4b97359870222611934be6884115493f9a017cc9f3543afd289ae67","source":{"kind":"arxiv","id":"1402.0851","version":2},"attestation_state":"computed","paper":{"title":"Interval scheduling and colorful independent sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Mathias Weller, Matthias Mnich, Ren\\'e van Bevern, Rolf Niedermeier","submitted_at":"2014-02-04T20:13:32Z","abstract_excerpt":"Numerous applications in scheduling, such as resource allocation or steel manufacturing, can be modeled using the NP-hard Independent Set problem (given an undirected graph and an integer k, find a set of at least k pairwise non-adjacent vertices). Here, one encounters special graph classes like 2-union graphs (edge-wise unions of two interval graphs) and strip graphs (edge-wise unions of an interval graph and a cluster graph), on which Independent Set remains NP-hard but admits constant-ratio approximations in polynomial time. We study the parameterized complexity of Independent Set on 2-unio"},"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":"1402.0851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-02-04T20:13:32Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"c61602119365863d7ed806d9cf1b033c1cb3e3ac90fc695d8bdfd11cd42961cd","abstract_canon_sha256":"6f562bd21e0203114ef9b3fef29f793bbe09b0ecba287c1fba43fe2219ee9b3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:09.027296Z","signature_b64":"sAId1mSuZKwrzby+P5iYLOBnVmTHO4KqXl79/Lw/SKUwP34PcrQXNJIIDSp628gHLBTkTMuJnjryaX6Jhm/LBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3f0fb3cd4b97359870222611934be6884115493f9a017cc9f3543afd289ae67","last_reissued_at":"2026-05-18T01:23:09.026849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:09.026849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interval scheduling and colorful independent sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Mathias Weller, Matthias Mnich, Ren\\'e van Bevern, Rolf Niedermeier","submitted_at":"2014-02-04T20:13:32Z","abstract_excerpt":"Numerous applications in scheduling, such as resource allocation or steel manufacturing, can be modeled using the NP-hard Independent Set problem (given an undirected graph and an integer k, find a set of at least k pairwise non-adjacent vertices). Here, one encounters special graph classes like 2-union graphs (edge-wise unions of two interval graphs) and strip graphs (edge-wise unions of an interval graph and a cluster graph), on which Independent Set remains NP-hard but admits constant-ratio approximations in polynomial time. We study the parameterized complexity of Independent Set on 2-unio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0851","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":"1402.0851","created_at":"2026-05-18T01:23:09.026921+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.0851v2","created_at":"2026-05-18T01:23:09.026921+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0851","created_at":"2026-05-18T01:23:09.026921+00:00"},{"alias_kind":"pith_short_12","alias_value":"2PYPWPGUXFZV","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2PYPWPGUXFZVTBYC","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2PYPWPGU","created_at":"2026-05-18T12:28:11.866339+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/2PYPWPGUXFZVTBYCEJQRSNF6NC","json":"https://pith.science/pith/2PYPWPGUXFZVTBYCEJQRSNF6NC.json","graph_json":"https://pith.science/api/pith-number/2PYPWPGUXFZVTBYCEJQRSNF6NC/graph.json","events_json":"https://pith.science/api/pith-number/2PYPWPGUXFZVTBYCEJQRSNF6NC/events.json","paper":"https://pith.science/paper/2PYPWPGU"},"agent_actions":{"view_html":"https://pith.science/pith/2PYPWPGUXFZVTBYCEJQRSNF6NC","download_json":"https://pith.science/pith/2PYPWPGUXFZVTBYCEJQRSNF6NC.json","view_paper":"https://pith.science/paper/2PYPWPGU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.0851&json=true","fetch_graph":"https://pith.science/api/pith-number/2PYPWPGUXFZVTBYCEJQRSNF6NC/graph.json","fetch_events":"https://pith.science/api/pith-number/2PYPWPGUXFZVTBYCEJQRSNF6NC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2PYPWPGUXFZVTBYCEJQRSNF6NC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2PYPWPGUXFZVTBYCEJQRSNF6NC/action/storage_attestation","attest_author":"https://pith.science/pith/2PYPWPGUXFZVTBYCEJQRSNF6NC/action/author_attestation","sign_citation":"https://pith.science/pith/2PYPWPGUXFZVTBYCEJQRSNF6NC/action/citation_signature","submit_replication":"https://pith.science/pith/2PYPWPGUXFZVTBYCEJQRSNF6NC/action/replication_record"}},"created_at":"2026-05-18T01:23:09.026921+00:00","updated_at":"2026-05-18T01:23:09.026921+00:00"}