Algorithms for Consistent Dynamic Labeling of Maps With a Time-Slider Interface

User interfaces for inspecting spatio-temporal events often allow their users to filter the events by specifying a time window with a time slider. We consider the case that filtered events are visualized on a map using textual or iconic labels. However, to ensure a clear visualization, not all filte...

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Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics Vol. 31; no. 10; pp. 6691 - 6704
Main Authors: Bonerath, Annika, Driemel, Anne, Haunert, Jan-Henrik, Haverkort, Herman, Langetepe, Elmar, Niedermann, Benjamin
Format: Journal Article
Language:English
Published: United States IEEE 01.10.2025
Subjects:
Annotations
approximation algorithm
Approximation algorithms
Data structures
Data visualization
dynamic query interface
Earthquakes
Heuristic algorithms
Labeling
Map labeling
Reproducibility of results
Spatial databases
temporal consistency
time-window query
Tornadoes
ISSN:1077-2626, 1941-0506, 1941-0506
Online Access:Get full text
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Summary:User interfaces for inspecting spatio-temporal events often allow their users to filter the events by specifying a time window with a time slider. We consider the case that filtered events are visualized on a map using textual or iconic labels. However, to ensure a clear visualization, not all filtered events are annotated with a label. We present algorithms for setting up a data structure that encodes for every possible time window the set of displayed labels. Our algorithms ensure that the displayed labels never overlap and guarantee the stability of the labeling during certain basic interactions with the time slider. Assuming that the labels have different priorities (weights), we aim to maximize the weight of the displayed labels integrated over all possible time windows. As basic interactions, we consider moving the entire time window, symmetrically scaling it, and dragging one of its endpoints. We consider two stability requirements: (1) during a basic interaction, a label should appear and disappear at most once; (2) if a label is displayed for a time window <inline-formula><tex-math notation="LaTeX">Q</tex-math> <mml:math><mml:mi>Q</mml:mi></mml:math><inline-graphic xlink:href="bonerath-ieq1-3527582.gif"/> </inline-formula>, then it is also displayed for all the time windows contained in <inline-formula><tex-math notation="LaTeX">Q</tex-math> <mml:math><mml:mi>Q</mml:mi></mml:math><inline-graphic xlink:href="bonerath-ieq2-3527582.gif"/> </inline-formula> and that contain its timestamp. We prove that finding an optimal solution is NP-hard and propose efficient constant-factor approximation algorithms for unit-square and unit-disk labels, as well as a fast greedy heuristic for arbitrarily shaped labels. In experiments on real-world data, we compare the non-exact algorithms with an exact approach through integer linear programming.
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ISSN:1077-2626
1941-0506
1941-0506
DOI:10.1109/TVCG.2025.3527582