{"paper":{"title":"Computing Covers of Plane Forests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alexis Beingessner, Luis Barba, Michiel H. M. Smid, Prosenjit Bose","submitted_at":"2013-11-19T20:06:51Z","abstract_excerpt":"Let $\\phi$ be a function that maps any non-empty subset $A$ of $\\mathbb{R}^2$ to a non-empty subset $\\phi(A)$ of $\\mathbb{R}^2$. A $\\phi$-cover of a set $T=\\{T_1, T_2, \\dots, T_m\\}$ of pairwise non-crossing trees in the plane is a set of pairwise disjoint connected regions such that each tree $T_i$ is contained in some region of the cover, and each region of the cover is either (1) $\\phi(T_i)$ for some $i$, or (2) $\\phi(A \\cup B)$, where $A$ and $B$ are constructed by either (1) or (2), and $A \\cap B \\neq \\emptyset$.\n  We present two properties for the function $\\phi$ that make the $\\phi$-cove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4860","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":""},"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"}