LR-Drawings of Ordered Rooted Binary Trees and Near-Linear Area Drawings of Outerplanar Graphs
Fabrizio Frati, Maurizio Patrignani, Vincenzo Roselli

TL;DR
This paper advances the understanding of LR-drawings for ordered rooted binary trees by providing optimal width algorithms, establishing new lower bounds, and connecting these results to outerplanar graph drawings with near-linear area.
Contribution
It introduces an algorithm for constructing minimum-width LR-drawings in sub-quadratic time and relates LR-drawings to outerplanar graph drawings, improving area bounds.
Findings
Optimal LR-drawings with minimum width can be constructed in O(n^1.48) time.
There exist trees requiring Omega(n^0.418) width in any LR-drawing.
Outerplanar graphs can be drawn in near-linear area using the structural decomposition of trees.
Abstract
In this paper we study a family of algorithms, introduced by Chan [SODA 1999] and called LR-algorithms, for drawing ordered rooted binary trees. In particular, we are interested in constructing LR-drawings (that are drawings obtained via LR-algorithms) with small width. Chan showed three different LR-algorithms that achieve, for an ordered rooted binary tree with nodes, width , width , and width . We prove that, for every -node ordered rooted binary tree, an LR-drawing with minimum width can be constructed in time. Further, we show an infinite family of -node ordered rooted binary trees requiring width in any LR-drawing; no lower bound better than was previously known. Finally, we present the results of an experimental evaluation that allowed us to determine the minimum width of all the…
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research · Digital Image Processing Techniques
