{"paper":{"title":"Drawing a Rooted Tree as a Rooted $y-$Monotone Minimum Spanning Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Konstantinos Mastakas","submitted_at":"2018-06-12T19:03:53Z","abstract_excerpt":"Given a rooted point set $P$, the rooted $y-$Monotone Minimum Spanning Tree (rooted $y-$MMST) of $P$ is the spanning geometric graph of $P$ in which all the vertices are connected to the root by some $y-$monotone path and the sum of the Euclidean lengths of its edges is the minimum. We show that the maximum degree of a rooted $y-$MMST is not bounded by a constant number. We give a linear time algorithm that draws any rooted tree as a rooted $y-$MMST and also show that there exist rooted trees that can be drawn as rooted $y-$MMSTs only in a grid of exponential area."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04720","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"}