Two-Sided boundary labeling with adjacent sides

Authors:
Philipp Kindermann;Benjamin Niedermann;Ignaz Rutter;Marcus Schaefer;André Schulz;Alexander Wolff
Affiliations:
Lehrstuhl für Informatik I, Universität Würzburg, Germany;Fakultät für Informatik, Karlsruher Institut für Technologie (KIT), Germany;Fakultät für Informatik, Karlsruher Institut für Technologie (KIT), Germany;College of Computing and Digital Media, DePaul University, Chicago, IL;Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Germany;Lehrstuhl für Informatik I, Universität Würzburg, Germany
Venue:
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Year:
2013

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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 problem Two-Sided Boundary Labeling with Adjacent Sides, where labels lie on two adjacent 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 that labels lie on one side or on two opposite sides of R (where a crossing-free solution always exists). For the more difficult case where labels lie on adjacent sides, we show how to compute crossing-free leader layouts that maximize the number of labeled points or minimize the total leader length.