{"paper":{"title":"The guillotine approach for TSP with neighborhoods revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Sophie Spirkl","submitted_at":"2013-12-02T09:06:32Z","abstract_excerpt":"The Euclidean TSP with neighborhoods (TSPN) is the following problem: Given a set R of k regions, find a shortest tour that visits at least one point from each region. We study the special cases of disjoint, connected, alpha-fat regions (i.e., every region P contains a disk of diameter diam(P)/alpha) and disjoint unit disks.\n  For the latter, Dumitrescu and Mitchell proposed an algorithm based on Mitchell's guillotine subdivision approach for the Euclidean TSP and claimed it to be a PTAS. However, their proof contains a severe gap, which we will close in the following. Bodlaender et al. remark"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0378","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"}