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Strict Upward Planar Grid Drawings of Binary Trees with Minimal Area (Poster Abstract)

Author Maarten Löffler

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Upward drawings
  • grid drawings
  • minimal area

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Abstract

Given a rooted binary tree T and a tuple (w, h), we wish to test whether there exists a strict upward drawing of T on a w × h grid; that is, a planar grid drawing with straight-line edges where every vertex has a strictly lower y-coordinate than its parent.

[Biedl and Mondal, 2017] prove that this problem is NP-hard for general trees; their construction crucially uses nodes of very high degree. [Akatiya et al., 2018] prove that the problem is also NP-hard for binary trees with a fixed combinatorial embedding; their construction crucially relies on the fixed embedding. Both pose the question for binary trees and a free embedding as an open problem.

Here, we show that this problem is also NP-hard.

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Maarten Löffler. Strict Upward Planar Grid Drawings of Binary Trees with Minimal Area (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 47:1-47:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.GD.2024.47

Author Details

Maarten Löffler
  • Utrecht University, The Netherlands

References

  1. Hugo Akitaya, Maarten Löffler, and Irene Parada. How to fit a tree in a box. Graphs and Combinatorics, 2022. Google Scholar
  2. Therese Biedl and Debajyoti Mondal. On upward drawings of trees on a given grid. In Fabrizio Frati and Kwan-Liu Ma, editors, Graph Drawing and Network Visualization, pages 318-325, Cham, 2018. Springer International Publishing. Google Scholar
  3. Thomas J. Schaefer. The complexity of satisfiability problems. In Proceedings of the Tenth Annual ACM Symposium on Theory of Computing, STOC '78, pages 216-226, New York, NY, USA, 1978. Association for Computing Machinery. URL: https://doi.org/10.1145/800133.804350.
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