{"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"}