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Universal Slope Sets for Upward Planar Drawings

  • Michael A. Bekos
  • Emilio Di GiacomoEmail author
  • Walter Didimo
  • Giuseppe Liotta
  • Fabrizio Montecchiani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)

Abstract

We prove that every set \(\mathcal {S}\) of \(\varDelta \) slopes containing the horizontal slope is universal for 1-bend upward planar drawings of bitonic st-graphs with maximum vertex degree \(\varDelta \), i.e., every such digraph admits a 1-bend upward planar drawing whose edge segments use only slopes in \(\mathcal {S}\). This result is worst-case optimal in terms of the number of slopes, and, for a suitable choice of \(\mathcal {S}\), it gives rise to drawings with worst-case optimal angular resolution. In addition, we prove that every such set \(\mathcal {S}\) can be used to construct 2-bend upward planar drawings of n-vertex planar st-graphs with at most \(4n-9\) bends in total. Our main tool is a constructive technique that runs in linear time.

Notes

Acknowledgments

Research partially supported by project: “Algoritmi e sistemi di analisi visuale di reti complesse e di grandi dimensioni - Ricerca di Base 2018, Dipartimento di Ingegneria, Università degli Studi di Perugia”.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Michael A. Bekos
    • 1
  • Emilio Di Giacomo
    • 2
    Email author
  • Walter Didimo
    • 2
  • Giuseppe Liotta
    • 2
  • Fabrizio Montecchiani
    • 2
  1. 1.Institut für InformatikUniversität TübingenTübingenGermany
  2. 2.Dipartimento di IngegneriaUniversità degli Studi di PerugiaPerugiaItaly

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