Evaluation of Labeling Strategies for Rotating Maps

We consider the following problem of labeling points in a dynamic map that allows rotation. We are given a set of points in the plane labeled by a set of mutually disjoint labels, where each label is an axis-aligned rectangle attached with one corner to its respective point. We require that each label remains horizontally aligned during the map rotation and our goal is to find a set of mutually non-overlapping active labels for every rotation angle $\alpha \in [0, 2\pi)$ so that the number of active labels over a full map rotation of 2$\pi$ is maximized. We discuss and experimentally evaluate several labeling models that define additional consistency constraints on label activities in order to reduce flickering effects during monotone map rotation. We introduce three heuristic algorithms and compare them experimentally to an existing approximation algorithm and exact solutions obtained from an integer linear program. Our results show that on the one hand low flickering can be achieved at the expense of only a small reduction in the objective value, and that on the other hand the proposed heuristics achieve a high labeling quality significantly faster than the other methods.Comment: 16 pages, extended version of a SEA 2014 pape

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 NP-complete and 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.Comment: 19 pages, 7 figures, extended version of a paper to appear at ISAAC 201

GraphMaps: Browsing Large Graphs as Interactive Maps

Algorithms for laying out large graphs have seen significant progress in the past decade. However, browsing large graphs remains a challenge. Rendering thousands of graphical elements at once often results in a cluttered image, and navigating these elements naively can cause disorientation. To address this challenge we propose a method called GraphMaps, mimicking the browsing experience of online geographic maps. GraphMaps creates a sequence of layers, where each layer refines the previous one. During graph browsing, GraphMaps chooses the layer corresponding to the zoom level, and renders only those entities of the layer that intersect the current viewport. The result is that, regardless of the graph size, the number of entities rendered at each view does not exceed a predefined threshold, yet all graph elements can be explored by the standard zoom and pan operations. GraphMaps preprocesses a graph in such a way that during browsing, the geometry of the entities is stable, and the viewer is responsive. Our case studies indicate that GraphMaps is useful in gaining an overview of a large graph, and also in exploring a graph on a finer level of detail.Comment: submitted to GD 201

Labeling Points of Interest in Dynamic Maps using Disk Labels

Dynamic maps which support panning, rotating and zooming are available on every smartphone today. To label geographic features on these maps such that the user is presented with a consistent map view even on map interaction is a challenge. We are presenting a map labeling scheme, which allows to label maps at an interactive speed. For any possible map rotation the computed labeling remains free of intersections between labels. It is not required to remove labels from the map view to ensure this. The labeling scheme supports map panning and continuous zooming. During zooming a label appears and disappears only once. When zooming out of the map a label disappears only if it may overlap an equally or more important label in an arbitrary map rotation. This guarantees that more important labels are preferred to less important labels on small scale maps. We are presenting some extensions to the labeling that could be used for more sophisticated labeling features such as area labels turning into point labels at smaller map scales. The proposed labeling scheme relies on a preprocessing phase. In this phase for each label the map scale where it is removed from the map view is computed. During the phase of map presentation the precomputed label set must only be filtered, what can be done very fast. We are presenting some hints that allow to efficiently compute the labeling in the preprocessing phase. Using these a labeling of about 11 million labels can be computed in less than 20 minutes. We are also presenting a datastructure to efficiently filter the precomputed label set in the interaction phase

Dispersive Elastodynamics of 1D Banded Materials and Structures: Design

Within periodic materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. In an earlier paper, the elastodynamics of one-dimensional periodic materials and finite structures comprising these materials were examined with an emphasis on their frequency-dependent characteristics. In this work, a novel design paradigm is presented whereby periodic unit cells are designed for desired frequency band properties, and with appropriate scaling, these cells are used as building blocks for forming fully periodic or partially periodic structures with related dynamical characteristics. Through this multiscale dispersive design methodology, which is hierarchical and integrated, structures can be devised for effective vibration or shock isolation without needing to employ dissipative damping mechanisms. The speed of energy propagation in a designed structure can also be dictated through synthesis of the unit cells. Case studies are presented to demonstrate the effectiveness of the methodology for several applications. Results are given from sensitivity analyses that indicate a high level of robustness to geometric variation.Comment: 33 text pages, 27 figure