{"paper":{"title":"Tree Drawings Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Timothy M. Chan","submitted_at":"2018-03-19T22:40:08Z","abstract_excerpt":"We make progress on a number of open problems concerning the area requirement for drawing trees on a grid. We prove that\n  1. every tree of size $n$ (with arbitrarily large degree) has a straight-line drawing with area $n2^{O(\\sqrt{\\log\\log n\\log\\log\\log n})}$, improving the longstanding $O(n\\log n)$ bound;\n  2. every tree of size $n$ (with arbitrarily large degree) has a straight-line upward drawing with area $n\\sqrt{\\log n}(\\log\\log n)^{O(1)}$, improving the longstanding $O(n\\log n)$ bound;\n  3. every binary tree of size $n$ has a straight-line orthogonal drawing with area $n2^{O(\\log^*n)}$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07185","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"}