{"paper":{"title":"Drawing Trees with Perfect Angular Resolution and Polynomial Area","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Christian A. Duncan, David Eppstein, Martin N\\\"ollenburg, Michael T. Goodrich, Stephen G. Kobourov","submitted_at":"2010-09-03T04:17:19Z","abstract_excerpt":"We study methods for drawing trees with perfect angular resolution, i.e., with angles at each node v equal to 2{\\pi}/d(v). We show:\n  1. Any unordered tree has a crossing-free straight-line drawing with perfect angular resolution and polynomial area.\n  2. There are ordered trees that require exponential area for any crossing-free straight-line drawing having perfect angular resolution.\n  3. Any ordered tree has a crossing-free Lombardi-style drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0581","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"}