{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DOY2VO66OSVYYMR6RUSKHOUMUQ","short_pith_number":"pith:DOY2VO66","schema_version":"1.0","canonical_sha256":"1bb1aabbde74ab8c323e8d24a3ba8ca409b9f97946e7ef02cba72c45e6c6412d","source":{"kind":"arxiv","id":"1509.08285","version":3},"attestation_state":"computed","paper":{"title":"The Continuous 1.5D Terrain Guarding Problem: Discretization, Optimal Solutions, and PTAS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Christiane Schmidt, James King, Michael Hemmer, Stephan Friedrichs","submitted_at":"2015-09-28T11:59:48Z","abstract_excerpt":"In the NP-hard continuous 1.5D Terrain Guarding Problem (TGP) we are given an $x$-monotone chain of line segments in $\\mathbb{R}^2$ (the terrain $T$) and ask for the minimum number of guards (located anywhere on $T$) required to guard all of $T$. We construct guard candidate and witness sets $G, W \\subset T$ of polynomial size such that any feasible (optimal) guard cover $G^* \\subseteq G$ for $W$ is also feasible (optimal) for the continuous TGP. This discretization allows us to (1) settle NP-completeness for the continuous TGP, (2) provide a Polynomial Time Approximation Scheme (PTAS) for the"},"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":"1509.08285","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-09-28T11:59:48Z","cross_cats_sorted":[],"title_canon_sha256":"52f3c8235884f659e87fcc92912e13a8675db5b0b1fad1bdddd0156a34cd1c56","abstract_canon_sha256":"7fc55525cbf53f691ee33573ade09b1bd85d88d6e7961aafddd627811956fa65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:55.003285Z","signature_b64":"3Bs5CBYlzOmiydavGDvz+qYXq4J4NHQYEsaOktOd9E6sTnI6+4FaZ40/T6M6/knJbQBp7tFsGWecax3eSPZ2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bb1aabbde74ab8c323e8d24a3ba8ca409b9f97946e7ef02cba72c45e6c6412d","last_reissued_at":"2026-05-18T01:11:55.002936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:55.002936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Continuous 1.5D Terrain Guarding Problem: Discretization, Optimal Solutions, and PTAS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Christiane Schmidt, James King, Michael Hemmer, Stephan Friedrichs","submitted_at":"2015-09-28T11:59:48Z","abstract_excerpt":"In the NP-hard continuous 1.5D Terrain Guarding Problem (TGP) we are given an $x$-monotone chain of line segments in $\\mathbb{R}^2$ (the terrain $T$) and ask for the minimum number of guards (located anywhere on $T$) required to guard all of $T$. We construct guard candidate and witness sets $G, W \\subset T$ of polynomial size such that any feasible (optimal) guard cover $G^* \\subseteq G$ for $W$ is also feasible (optimal) for the continuous TGP. This discretization allows us to (1) settle NP-completeness for the continuous TGP, (2) provide a Polynomial Time Approximation Scheme (PTAS) for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08285","kind":"arxiv","version":3},"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":"1509.08285","created_at":"2026-05-18T01:11:55.002995+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.08285v3","created_at":"2026-05-18T01:11:55.002995+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08285","created_at":"2026-05-18T01:11:55.002995+00:00"},{"alias_kind":"pith_short_12","alias_value":"DOY2VO66OSVY","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DOY2VO66OSVYYMR6","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DOY2VO66","created_at":"2026-05-18T12:29:17.054201+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/DOY2VO66OSVYYMR6RUSKHOUMUQ","json":"https://pith.science/pith/DOY2VO66OSVYYMR6RUSKHOUMUQ.json","graph_json":"https://pith.science/api/pith-number/DOY2VO66OSVYYMR6RUSKHOUMUQ/graph.json","events_json":"https://pith.science/api/pith-number/DOY2VO66OSVYYMR6RUSKHOUMUQ/events.json","paper":"https://pith.science/paper/DOY2VO66"},"agent_actions":{"view_html":"https://pith.science/pith/DOY2VO66OSVYYMR6RUSKHOUMUQ","download_json":"https://pith.science/pith/DOY2VO66OSVYYMR6RUSKHOUMUQ.json","view_paper":"https://pith.science/paper/DOY2VO66","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.08285&json=true","fetch_graph":"https://pith.science/api/pith-number/DOY2VO66OSVYYMR6RUSKHOUMUQ/graph.json","fetch_events":"https://pith.science/api/pith-number/DOY2VO66OSVYYMR6RUSKHOUMUQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DOY2VO66OSVYYMR6RUSKHOUMUQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DOY2VO66OSVYYMR6RUSKHOUMUQ/action/storage_attestation","attest_author":"https://pith.science/pith/DOY2VO66OSVYYMR6RUSKHOUMUQ/action/author_attestation","sign_citation":"https://pith.science/pith/DOY2VO66OSVYYMR6RUSKHOUMUQ/action/citation_signature","submit_replication":"https://pith.science/pith/DOY2VO66OSVYYMR6RUSKHOUMUQ/action/replication_record"}},"created_at":"2026-05-18T01:11:55.002995+00:00","updated_at":"2026-05-18T01:11:55.002995+00:00"}