Benjamin Niedermann

Trajectory-Based Dynamic Map Labeling

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 maximization problem in this model. The problem is \(\cal NP\)-complete and \(\mathcal W[1]\)-hard. In the restricted, yet practically relevant case that no more than k labels can be active at any time, we give polynomial-time algorithms. For the general case we present a practical ILP formulation with an experimental evaluation as well as approximation algorithms.

Using ILP/SAT to Determine Pathwidth, Visibility Representations, and other Grid-Based Graph Drawings

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 problem-specific constraints. We describe a general d-dimensional model for grid representation problems. This model can be used to solve a variety of NP-hard graph problems, including pathwidth, bandwidth, optimum st-orientation, area-minimal bar-k visibility representation, boxicity-k graphs and others. We implemented SAT-models for all of the above problems and evaluated them on the Rome graphs collection. The experiments show that our model successfully solves NP-hard problems within few minutes on small to medium-size Rome graphs.

Two-Sided boundary labeling with adjacent sides

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.

Label Placement in Road Maps

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 that this is NP-hard in general, but the problem can be solved in polynomial time if the road map is an embedded tree.

On the readability of leaders in boundary labeling

External labeling deals with annotating features in images with labels that are placed outside of the image and are connected by curves (so-called leaders) to the corresponding features. While external labeling has been extensively investigated from a perspective of automatization, the research on its readability has been neglected. In this article, we present the first formal user study on the readability of leader types in boundary labeling, a special variant of external labeling that considers rectangular image contours. We consider the four most studied leader types (straight, L-shaped, diagonal, and S-shaped) with respect to their performance, that is, whether and how fast a viewer can assign a feature to its label and vice versa. We give a detailed analysis of the results regarding the readability of the four models and discuss their aesthetic qualities based on the users’ preference judgments and interviews. As a consequence of our experiment, we can generally recommend L-shaped leaders as the best compromise between measured task performance and subjective preference ratings, while straight and diagonal leaders received mixed ratings in the two measures. S-shaped leaders are generally not recommended from a practical point of view.

An Algorithmic Framework for Labeling Network Maps

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 labeling a single line of the network is NP-hard, even if we make very restricting requirements about the labeling style that is used with this model. For a restricted variant of that model, we then introduce an efficient algorithm that optimally labels a single line with respect to a given cost function. Based on that algorithm, we present a general and sophisticated workflow for multiple metro lines, which is experimentally evaluated on real-world metro maps.

Radial contour labeling with straight leaders

The usefulness of technical drawings as well as scientific illustrations such as medical drawings of human anatomy essentially depends on the placement of labels that describe all relevant parts of the figure. In order to not spoil or clutter the figure with text, the labels are often placed around the figure and are associated by thin connecting lines to their features, respectively. This labeling technique is known as external label placement. In this paper we introduce a flexible and general approach for external label placement assuming a contour of the figure prescribing the possible positions of the labels. While much research on external label placement aims for fast labeling procedures for interactive systems, we focus on highest-quality illustrations. Based on interviews with domain experts and a semi-automatic analysis of 202 handmade anatomical drawings, we identify a set of 18 layout quality criteria, naturally not all of equal importance. We design a new geometric label placement algorithm that is based only on the most important criteria. Yet, other criteria can flexibly be included in the algorithm, either as hard constraints not to be violated or as soft constraints whose violation is penalized by a general cost function. We formally prove that our approach yields labelings that satisfy all hard constraints and have minimum overall cost. Introducing several speedup techniques, we further demonstrate how to deploy our approach in practice. In an experimental evaluation on real-world anatomical drawings we show that the resulting labelings are of high quality and can be produced in adequate time.

Inferring the Parametric Weight of a Bicriteria Routing Model from Trajectories

Finding a shortest path between two nodes in a graph is a well-studied problem whose applicability in practice crucially relies on the choice of the applied cost function. Especially, for the key application of vehicle routing the cost function may consist of more than one optimization criterion (e.g., distance, travel time, etc.). Finding a good balance between these criteria is a challenging and essential task. We present an approach that learns that balance from existing GPS-tracks. The core of our approach is to find a balance factor α for a given set of GPS-tracks such that the tracks can be decomposed into a minimum number of optimal paths with respect to α. In an experimental evaluation on real-world GPS-tracks of bicyclists we show that our approach yields an appropriate balance factor in a reasonable amount of time.

An Algorithmic Framework for Labeling Road Maps

Given an unlabeled road map, we consider, from an algorithmic perspective, the cartographic problem of placing non-overlapping road labels embedded in the roads. We first decompose the road network into logically coherent road sections, i.e., parts of roads between two junctions. Based on this decomposition, we present and implement a new and versatile framework for placing labels in road maps such that the number of labeled road sections is maximized. In an experimental evaluation with road maps of 11 major cities we show that our proposed labeling algorithm is both fast in practice and that it reaches near-optimal solution quality, where optimal solutions are obtained by mixed-integer linear programming. In direct comparison, our algorithm consistently outperforms the standard OpenStreetMap renderer Mapnik.