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How to Fit a Tree in a Box

  • Hugo A. Akitaya
  • Maarten Löffler
  • Irene ParadaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)

Abstract

We study compact straight-line embeddings of trees. We show that perfect binary trees can be embedded optimally: a tree with \(n\) nodes can be drawn on a \(\sqrt{n}\) by \(\sqrt{n}\) grid. We also show that testing whether a given binary tree has an upward embedding with a given combinatorial embedding in a given grid is NP-hard.

Notes

Acknowledgements

This research was initiated at the 33rd Bellairs Winter Workshop on Computational Geometry in 2018. We would like to thank all participants of the workshop for fruitful discussions on the topic. H.A.A. was supported by NSF awards CCF-1422311 and CCF-1423615, and the Science Without Borders scholarship program. M.L. was partially supported by the Netherlands Organisation for Scientific Research (NWO) through grant number 614.001.504. I.P. was supported by the Austrian Science Fund (FWF) grant W1230.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Hugo A. Akitaya
    • 1
  • Maarten Löffler
    • 2
  • Irene Parada
    • 3
    Email author
  1. 1.Tufts UniversityMedfordUSA
  2. 2.Utrecht UniversityUtrechtThe Netherlands
  3. 3.Graz University of TechnologyGrazAustria

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