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In this paper we introduce trajectory-based labeling, a new variant of dynamic map labeling, where a movement trajectory for the map viewport is given. We define a general labeling model and study the active range maximiza-tion problem in this model. The problem is N P-complete and W[1]-hard. In the restricted, yet practically relevant case that no more… (More)

Drawing network maps automatically comprises two challenging steps, namely laying out the map and placing non-overlapping labels. In this paper we tackle the problem of labeling an already existing network map considering the application of metro maps. We present a flexible and versatile labeling model that subsumes different labeling styles. We show that… (More)

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 polygonal paths, so-called leaders. In this paper, we study the Two-Sided… (More)

A road map can be interpreted as a graph embedded in the plane, in which each vertex corresponds to a road junction and each edge to a particular road section. We consider the cartographic problem to place non-overlapping road labels along the edges so that as many road sections as possible are identified by their name, i.e., covered by a label. We show… (More)

We present a simple and versatile formulation of grid-based graph representation problems as an integer linear program (ILP) and a corresponding SAT instance. In a grid-based representation vertices and edges correspond to axis-parallel boxes on an underlying integer grid; boxes can be further constrained in their shapes and interactions by additional… (More)

Boundary labeling deals with annotating features in images such that labels are placed outside of the image and are connected by curves (so-called leaders) to the corresponding features. While boundary labeling has been extensively investigated from an algorithmic perspective, the research on its readability has been neglected. In this paper we present the… (More)

Given an unlabeled road map, we consider, from an algorithmic perspective, the car-tographic problem to place non-overlapping road labels embedded in their roads. We first decompose the road network into logically coherent road sections, e.g., parts of roads between two junctions. Based on this decomposition, we present and implement a new and versatile… (More)

The increased availability of interactive maps on the Internet and on personal mobile devices has created new challenges in computational cartography and, in particular, for label placement in maps. Operations like rotation, zoom, and translation dynamically change the map over time and make a consistent adaptation of the map labeling necessary. In this… (More)

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… (More)

- Benjamin Niedermann, Martin Nöllenburg, Therese Biedl, Stefan Felsner, Michael Kaufmann, Stephen G Kobourov +5 others
- 2015

Die folgende Tabelle zeigt ergänzend zu den Angaben auf der Webseite, in welchen Teilen der Literatur die in der Vorlesung behandelten Beweise zu den Sätzen und Lemmas der Vorle-sungsfolien zu finden sind. Das soll das Auffinden der Beweise erleichtern. Allerdings kann es für das Verständnis durchaus sinnvoll sein, zusätzlich auch weitere Teile der… (More)