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Constrained Boundary Labeling

Authors Thomas Depian , Martin Nöllenburg , Soeren Terziadis , Markus Wallinger

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Author Details

Thomas Depian
  • Algorithms and Complexity Group, TU Wien, Austria
Martin Nöllenburg
  • Algorithms and Complexity Group, TU Wien, Austria
Soeren Terziadis
  • Algorithms cluster, TU Eindhoven, The Netherlands
Markus Wallinger
  • Chair for Efficient Algorithms, Technical University of Munich, Germany

Funding

  • Depian, Thomas: Vienna Science and Technology Fund (WWTF) [10.47379/ICT22029].
  • Nöllenburg, Martin: Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035].
  • Terziadis, Soeren: Vienna Science and Technology Fund (WWTF) [10.47379/ICT19035] and 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].

Cite As Get BibTex

Thomas Depian, Martin Nöllenburg, Soeren Terziadis, and Markus Wallinger. Constrained Boundary Labeling. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ISAAC.2024.26

Abstract

Boundary labeling is a technique in computational geometry used to label dense sets of feature points in an illustration. It involves placing labels along an axis-aligned bounding box and connecting each label with its corresponding feature point using non-crossing leader lines. Although boundary labeling is well-studied, semantic constraints on the labels have not been investigated thoroughly. In this paper, we introduce grouping and ordering constraints in boundary labeling: Grouping constraints enforce that all labels in a group are placed consecutively on the boundary, and ordering constraints enforce a partial order over the labels. We show that it is NP-hard to find a labeling for arbitrarily sized labels with unrestricted positions along one side of the boundary. However, we obtain polynomial-time algorithms if we restrict this problem either to uniform-height labels or to a finite set of candidate positions. Finally, we show that finding a labeling on two opposite sides of the boundary is NP-complete, even for uniform-height labels and finite label positions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Computational geometry
  • Theory of computation → Problems, reductions and completeness
  • Human-centered computing → Geographic visualization
Keywords
  • Boundary labeling
  • Grouping constraints
  • Ordering constraints

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