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Multi-sided Boundary Labeling

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Abstract

In the Boundary Labeling problem, we are given a set of n points, referred to as sites, inside an axis-parallel rectangle R, and a set of n pairwise disjoint rectangular labels that are attached to R from the outside. The task is to connect the sites to the labels by non-intersecting rectilinear paths, so-called leaders, with at most one bend. In this paper, we study the Multi-Sided Boundary Labeling problem, with labels lying on at least two sides of the enclosing rectangle. We present a polynomial-time algorithm that computes a crossing-free leader layout if one exists. So far, such an algorithm has only been known for the cases in which labels lie on one side or on two opposite sides of R (here a crossing-free solution always exists). The case where labels may lie on adjacent sides is more difficult. We present efficient algorithms for testing the existence of a crossing-free leader layout that labels all sites and also for maximizing the number of labeled sites in a crossing-free leader layout. For two-sided boundary labeling with adjacent sides, we further show how to minimize the total leader length in a crossing-free layout.

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Authors and Affiliations

  1. Lehrstuhl für Informatik I, Universität Würzburg, Würzburg, Germany

    Philipp Kindermann & Alexander Wolff

  2. Fakultät für Informatik, Karlsruher Institut für Technologie (KIT), Karlsruhe, Germany

    Benjamin Niedermann & Ignaz Rutter

  3. College of Computing and Digital Media, DePaul University, Chicago, IL, USA

    Marcus Schaefer

  4. Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Münster, Germany

    André Schulz

Authors
  1. Philipp Kindermann
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  2. Benjamin Niedermann
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  3. Ignaz Rutter
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  4. Marcus Schaefer
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  5. André Schulz
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  6. Alexander Wolff
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Corresponding author

Correspondence to Benjamin Niedermann.

Additional information

A preliminary version of this paper has appeared in Proc. 13th Int. Algorithms Data Struct. Symp. (WADS’13), volume 8037 of Lect. Notes Comput. Sci., pages 463–474, Springer-Verlag. This research was initiated during the GraDr Midterm meeting at the TU Berlin in October 2012. The meeting was supported by the ESF EuroGIGA networking grant. Ph. Kindermann acknowledges support by the ESF EuroGIGA project GraDR (DFG Grant Wo 758/5-1).

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Kindermann, P., Niedermann, B., Rutter, I. et al. Multi-sided Boundary Labeling. Algorithmica 76, 225–258 (2016). https://doi.org/10.1007/s00453-015-0028-4

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