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Boundary Labeling in a Circular Orbit

Authors Annika Bonerath , Martin Nöllenburg , Soeren Terziadis , Markus Wallinger , Jules Wulms

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  • Human-centered computing → Visualization
  • Theory of computation → Computational geometry
Keywords
  • External labeling
  • Orthoradial drawing
  • NP-hardness
  • Polynomial algorithms

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Abstract

Boundary labeling is a well-known method for displaying short textual labels for a set of point features in a figure alongside the boundary of that figure. Labels and their corresponding points are connected via crossing-free leaders. We propose orbital boundary labeling as a new variant of the problem, in which (i) the figure is enclosed by a circular contour and (ii) the labels are placed as disjoint circular arcs in an annulus-shaped orbit around the contour. The algorithmic objective is to compute an orbital boundary labeling with the minimum total leader length. We identify several parameters that define the corresponding problem space: two leader types (straight or orbital-radial), label size and order, presence of candidate label positions, and constraints on where a leader attaches to its label. Our results provide polynomial-time algorithms for many variants and NP-hardness for others, using a variety of geometric and combinatorial insights.

Cite As Get BibTex

Annika Bonerath, Martin Nöllenburg, Soeren Terziadis, Markus Wallinger, and Jules Wulms. Boundary Labeling in a Circular Orbit. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.GD.2024.22

Author Details

Annika Bonerath
  • University of Bonn, Germany
Martin Nöllenburg
  • Algorithms and Complexity Group, TU Wien, Austria
Soeren Terziadis
  • TU Eindhoven, The Netherlands
Markus Wallinger
  • Chair for Efficient Algorithms, TU Munich, Germany
Jules Wulms
  • TU Eindhoven, The Netherlands

Funding

  • Bonerath, Annika: German Research Foundation under Germany’s Excellence Strategy, EXC-2070 - 390732324 - PhenoRob.
  • Nöllenburg, Martin: Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035].
  • Terziadis, Soeren: Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035] and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No 101034253.
  • Wallinger, Markus: Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035].

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