Optimizing active ranges for consistent dynamic map labeling

Been, Ken; Nöllenburg, Martin; Poon, Sheung-Hung; Wolff, Alexander

doi:10.1016/j.comgeo.2009.03.006

Cited by 52 publications

(25 citation statements)

References 12 publications

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“…Labeling in dynamic maps is a very similar problem [Petzold et al 2003;Been et al 2006Been et al , 2010, which studies the placement of labels in a dynamically generated map to avoid overlaps among labels. The number of labels is typically assumed to be too large for displaying all of them in the limited space, and an appropriate selection and placing of labels has to be performed at an interactive speed.…”

Section: Related Workmentioning

confidence: 99%

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Consistent thinning of large geographical data for map visualization

Sarma

Lee

González

et al. 2013

ACM Trans. Database Syst.

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Large-scale map visualization systems play an increasingly important role in presenting geographic datasets to end-users. Since these datasets can be extremely large, a map rendering system often needs to select a small fraction of the data to visualize them in a limited space. This article addresses the fundamental challenge of thinning: determining appropriate samples of data to be shown on specific geographical regions and zoom levels. Other than the sheer scale of the data, the thinning problem is challenging because of a number of other reasons: (1) data can consist of complex geographical shapes, (2) rendering of data needs to satisfy certain constraints, such as data being preserved across zoom levels and adjacent regions, and (3) after satisfying the constraints, an optimal solution needs to be chosen based on objectives such as maximality, fairness, and importance of data.This article formally defines and presents a complete solution to the thinning problem. First, we express the problem as an integer programming formulation that efficiently solves thinning for desired objectives. Second, we present more efficient solutions for maximality, based on DFS traversal of a spatial tree. Third, we consider the common special case of point datasets, and present an even more efficient randomized algorithm. Fourth, we show that contiguous regions are tractable for a general version of maximality for which arbitrary regions are intractable. Fifth, we examine the structure of our integer programming formulation and show that for point datasets, our program is integral. Finally, we have implemented all techniques from this article in Google Maps [Google 2005] visualizations of fusion tables [Gonzalez et al. 2010], and we describe a set of experiments that demonstrate the trade-offs among the algorithms.

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Section: Related Workmentioning

confidence: 99%

“…However, unique priorities among labels are assumed and the optimality is with regard to the priority, which greatly simplifies the problem. Approximation algorithms are studied in Been et al [2010] and their approximation factors are provided. None of the preceding works performed experimental evaluation with real-world datasets.…”

Section: Related Workmentioning

confidence: 99%

Consistent thinning of large geographical data for map visualization

Sarma

Lee

González

et al. 2013

ACM Trans. Database Syst.

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“…Continuous movement and zooming, however, are not explicitly supported by their methods and may lead to sudden discrete changes of label positions. Been et al [1,2] define consistency criteria for dynamic labelings that avoid popping and jumping of labels during movement and zooming. They show NP-hardness of maximizing the number of labels in a consistent labeling and present several approximation algorithms for the problem.…”

Section: Related Workmentioning

confidence: 99%

“…Any particular view R, whose aspect ratio r matches the aspect ratio ws/hs of the screen can be expressed by three extended world coordinates introduced by Been et al [2] for dynamic map labeling. The coordinates define a threedimensional (x, y, z)-space where the x-and y-coordinates are a position in the map plane, and the z-coordinate is a zoom level.…”

Section: Extensions Of the Modelmentioning

confidence: 99%

Dynamic one-sided boundary labeling

Nöllenburg

Polishchuk

Sysikaski

2010

Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems

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In boundary labeling, features on a map are connected to a stack of labels on the map boundary, using simple polylines called leaders. We consider the setting that the labels are axis-aligned non-overlapping rectangles placed on one side of the map, and leaders are rectilinear polylines with at most one bend. The goal is to find a labeling that minimizes the total length of the leaders.We introduce three extensions of the one-sided boundary labeling problem: (i) a dynamic setting for continuous scale changes, (ii) a clustered setting for multiple label stacks, and (iii) a combined dynamic clustered setting. We obtain the following results:• Optimal label placement as a function of map scale can be computed in O(n log n + σ log n) time, where σ is the number of "combinatorially different" labelings that occur during zooming. • In a map with fixed scale, an optimal clustered label placement can be found in O(n log n) time. • In O(n log 2 n + γ log n) time one can build a structure of size O(γ) representing the optimal clustered label placement for all possible map scales; here γ is, again, the number of combinatorially different labelings.We further extend our basic model to the case where labeled features enter or leave the viewport due to map panning and zooming. Our algorithms are based on combining standard computational-geometry tools and have been implemented in a Java applet (available online), which indicates that the algorithms are fast enough for interactive use without delays.

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“…Dynamic point labeling, however, has seen very few theoretical results. Been et al 5 studied number-maximization for points under zooming, giving constant-factor approximations for unit-square labels in the 1-position model. Gemsa et al 6 gave a PTAS for the same problem with rotation instead of zooming.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Point Labeling Is Strongly Pspace-Complete

Buchin

Gerrits

2014

Int. J. Comput. Geom. Appl.

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An important but strongly NP-hard problem in automated cartography is how to best place textual labels for point features on a static map. We examine the complexity of various generalizations of this problem for dynamic and/or interactive maps. Specifically, we show that it is strongly PSPACE-complete to decide whether there is a smooth dynamic labeling (function from time to static labelings) when the points move, when points are added and removed, or when the user pans, rotates, and/or zooms their view of the points. In doing so we develop a framework from which a wide variety of labeling hardness results can be obtained, including (next to the PSPACE-hardness results) both known and new results on the NP-hardness of static labeling.

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Optimizing active ranges for consistent dynamic map labeling

Cited by 52 publications

References 12 publications

Consistent thinning of large geographical data for map visualization

Consistent thinning of large geographical data for map visualization

Dynamic one-sided boundary labeling

Dynamic Point Labeling Is Strongly Pspace-Complete

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