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Internally-Convex Drawings of Outerplanar Graphs in Small Area

Authors Michael A. Bekos , Giordano Da Lozzo , Fabrizio Frati , Giuseppe Liotta , Antonios Symvonis

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LIPIcs.GD.2025.18.pdf
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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Mathematics of computing → Graph theory
Keywords
  • Grid drawings
  • convexity
  • area bounds
  • outerplanar graphs

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Abstract

A well-known result by Kant [Algorithmica, 1996] implies that n-vertex outerplane graphs admit embedding-preserving planar straight-line grid drawings where the internal faces are convex polygons in O(n²) area. In this paper, we present an algorithm to compute such drawings in O(n¹·⁵) area. We also consider outerplanar drawings in which the internal faces are required to be strictly-convex polygons. In this setting, we consider outerplanar graphs whose weak dual is a path and give a drawing algorithm that achieves Θ(nk²) area, where k is the maximum size of an internal facial cycle.

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Michael A. Bekos, Giordano Da Lozzo, Fabrizio Frati, Giuseppe Liotta, and Antonios Symvonis. Internally-Convex Drawings of Outerplanar Graphs in Small Area. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.18

Author Details

Michael A. Bekos
  • University of Ioannina, Greece
Giordano Da Lozzo
  • Roma Tre University, Italy
Fabrizio Frati
  • Roma Tre University, Italy
Giuseppe Liotta
  • University of Perugia, Italy
Antonios Symvonis
  • National Technical University of Athens, Greece

Funding

Bekos and Symvonis were supported by HFRI Grant No: 26320. Da Lozzo and Frati were supported by the European Union, Next Generation EU, Mission 4, Component 1, CUP J53D23007130006 PRIN proj. 2022ME9Z78 "NextGRAAL: Next-generation algorithms for constrained GRAph visuALization". Liotta was supported by MUR PON Proj. ARS01 00540 and by MUR PRIN Project no. 2022TS4Y3N.

References

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