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Nilsson, Christiane Schmidt, Christian Rieck, Omrit Filtser","submitted_at":"2026-06-24T13:31:27Z","abstract_excerpt":"Motivated by applications for robust guarding, we consider a variant of the multiple-watchmen problem that ensures that every point within a polygon $P$ is seen from more than one direction: we search for two routes $W_1,W_2$, such that every point $p\\in P$ is contained in a segment $\\overline{w_1w_2}\\subseteq P$ such that $w_1\\in W_1$ and $w_2\\in W_2$. We call such routes segment watchman routes.\n  We show that finding the two routes that are optimal with respect to the min-max criterion is weakly NP-hard even in simple polygons, and that finding the routes that are optimal with respect to th"},"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":"2606.25816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-06-24T13:31:27Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"cf05fc3f3a89784a0edd37c054473d750c8714689e55c843c6a54ffa175f3e80","abstract_canon_sha256":"8b49d922f1426ec139c80ce8799c1cd2f0aa969962f705aeeb6a0d6d64a75962"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:40.245131Z","signature_b64":"/2XUwzEK+SNQvXeUHeI6pklyn5eVafujjs9yhaPsJA2HIPpt/yfBUY8D2TxbKjhPWnR6Om2fKs0k9V2yRpwgDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e274dd3274a17d977753de9293307049d80b8104f2fc1adcafa96a57c3e9ca97","last_reissued_at":"2026-06-25T01:18:40.244680Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:40.244680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Segment Watchman Routes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Anna Br\\\"otzner, Bengt J. 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We call such routes segment watchman routes.\n  We show that finding the two routes that are optimal with respect to the min-max criterion is weakly NP-hard even in simple polygons, and that finding the routes that are optimal with respect to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25816","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/2606.25816/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":"2606.25816","created_at":"2026-06-25T01:18:40.244737+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.25816v1","created_at":"2026-06-25T01:18:40.244737+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.25816","created_at":"2026-06-25T01:18:40.244737+00:00"},{"alias_kind":"pith_short_12","alias_value":"4J2N2MTUUF6Z","created_at":"2026-06-25T01:18:40.244737+00:00"},{"alias_kind":"pith_short_16","alias_value":"4J2N2MTUUF6ZO52T","created_at":"2026-06-25T01:18:40.244737+00:00"},{"alias_kind":"pith_short_8","alias_value":"4J2N2MTU","created_at":"2026-06-25T01:18:40.244737+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/4J2N2MTUUF6ZO52T32JJGMDQJH","json":"https://pith.science/pith/4J2N2MTUUF6ZO52T32JJGMDQJH.json","graph_json":"https://pith.science/api/pith-number/4J2N2MTUUF6ZO52T32JJGMDQJH/graph.json","events_json":"https://pith.science/api/pith-number/4J2N2MTUUF6ZO52T32JJGMDQJH/events.json","paper":"https://pith.science/paper/4J2N2MTU"},"agent_actions":{"view_html":"https://pith.science/pith/4J2N2MTUUF6ZO52T32JJGMDQJH","download_json":"https://pith.science/pith/4J2N2MTUUF6ZO52T32JJGMDQJH.json","view_paper":"https://pith.science/paper/4J2N2MTU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.25816&json=true","fetch_graph":"https://pith.science/api/pith-number/4J2N2MTUUF6ZO52T32JJGMDQJH/graph.json","fetch_events":"https://pith.science/api/pith-number/4J2N2MTUUF6ZO52T32JJGMDQJH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4J2N2MTUUF6ZO52T32JJGMDQJH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4J2N2MTUUF6ZO52T32JJGMDQJH/action/storage_attestation","attest_author":"https://pith.science/pith/4J2N2MTUUF6ZO52T32JJGMDQJH/action/author_attestation","sign_citation":"https://pith.science/pith/4J2N2MTUUF6ZO52T32JJGMDQJH/action/citation_signature","submit_replication":"https://pith.science/pith/4J2N2MTUUF6ZO52T32JJGMDQJH/action/replication_record"}},"created_at":"2026-06-25T01:18:40.244737+00:00","updated_at":"2026-06-25T01:18:40.244737+00:00"}