The rooted tree embedding problem into points in the plane
type: Item
instance of: scholarly article
title: The rooted tree embedding problem into points in the plane
zbMATH Open document ID: 0791.05027
DOI: 10.1007/BF02573994
author: Micha A. Perles
author: Akihisa Tamura
author: Shinnichi Tokunaga
author: Yoshiko T. Ikebe
published in: Discrete \& Computational Geometry
publication date: 1994-06-20T00:00:00Z
full work available at URL: https://eudml.org/doc/131288
review text: Let \(T\) be a rooted tree with \(n\) vertices and \(N\) a set \(\{p_ 1,\dots,p_ n\}\) of \(n\) points in general position in \(\mathbb{R}^ 2\). Denote the sets of vertices and edges of \(T\) by \(V(T)\) and \(E(T)\), respectively. A bijection \(\varphi\) from \(V(T)\) to \(N\) satisfying the conditions: (C1) \(\varphi(r_ 1)=p_ 1\) \((r_ 1\) is the root of \(T)\), (C2) for nonadjacent edges \(u_ 1v_ 1\), \(u_ 2v_ 2 \in E(T)\), the line segments \(\overline {\varphi (u_ 1) \varphi(v_ 1)}\), \(\overline {\varphi (u_ 2) \varphi (v_ 2)}\) are disjoint, is called a rooted tree embedding (or \(rt\)-embedding). The main theorem states that an \(rt\)-embedding of \(V(T)\) on \(N\) always exists and that some \(rt\)-embedding can be constructed in polynomial time with respect to \(n\).
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 502907
zbMATH Keywords: algorithm
zbMATH Keywords: rooted tree
zbMATH Keywords: embedding
zbMATH Keywords: polynomial time
reviewed by: Stelian Mihalas
MaRDI profile type: Publication
cites work: Q3772828
cites work: Q3138292
cites work: Q3992847
OpenAlex ID: W2031303191
description: scientific article; zbMATH DE number 502907