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How Many Slopes Does Polynomial Area Cost?

Authors Michael A. Bekos , Eleni Katsanou , Philipp Kindermann , Maria Eleni Pavlidi

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LIPIcs.SWAT.2026.6.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorics
  • Mathematics of computing → Graph theory
  • Human-centered computing → Graph drawings
Keywords
  • k-bend planar drawings
  • planar slope number
  • area requirements

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Abstract

In this work, we study the interplay between the number of slopes, the number of bends per edge, and the area requirements for planar drawings of bounded-degree graphs. Our motivation stems from the fact that, while numerous algorithms produce planar drawings with few slopes for graphs of relatively small degree in polynomial area, existing approaches for higher-degree graphs often require super-polynomial area. We address this gap in the literature by presenting new constructions that yield polynomial-area drawings with few bends per edge while slightly increasing the required number of slopes, thereby providing the first systematic study of slopes, bends and area trade-offs.

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Michael A. Bekos, Eleni Katsanou, Philipp Kindermann, and Maria Eleni Pavlidi. How Many Slopes Does Polynomial Area Cost?. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SWAT.2026.6

Author Details

Michael A. Bekos
  • University of Ioannina, Greece
Eleni Katsanou
  • National Technical University of Athens, Greece
Philipp Kindermann
  • Trier University, Germany
Maria Eleni Pavlidi
  • University of Ioannina, Greece

Funding

This work was partially funded by the IKYDA 2025 funding program of the DAAD (project 57775422 "Algorithms and Combinatorics for Drawing Graphs with Few Slopes").

References

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