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.
@InProceedings{depian_et_al:LIPIcs.ISAAC.2024.26, author = {Depian, Thomas and N\"{o}llenburg, Martin and Terziadis, Soeren and Wallinger, Markus}, title = {{Constrained Boundary Labeling}}, booktitle = {35th International Symposium on Algorithms and Computation (ISAAC 2024)}, pages = {26:1--26:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-354-6}, ISSN = {1868-8969}, year = {2024}, volume = {322}, editor = {Mestre, Juli\'{a}n and Wirth, Anthony}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2024.26}, URN = {urn:nbn:de:0030-drops-221539}, doi = {10.4230/LIPIcs.ISAAC.2024.26}, annote = {Keywords: Boundary labeling, Grouping constraints, Ordering constraints} }
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