eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-05-31
24:1
24:16
10.4230/LIPIcs.SWAT.2024.24
article
Optimizing Symbol Visibility Through Displacement
Gärtner, Bernd
1
Kalani, Vishwas
2
M. Reddy, Meghana
1
https://orcid.org/0000-0001-9185-1246
Meulemans, Wouter
3
Speckmann, Bettina
3
https://orcid.org/0000-0002-8514-7858
Stojaković, Miloš
4
https://orcid.org/0000-0002-2545-8849
Department of Computer Science, ETH Zürich, Switzerland
Department of Computer Science and Engineering, I.I.T. Delhi, India
Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Serbia
In information visualization, the position of symbols often encodes associated data values. When visualizing data elements with both a numerical and a categorical dimension, positioning in the categorical axis admits some flexibility. This flexibility can be exploited to reduce symbol overlap, and thereby increase legibility. In this paper we initialize the algorithmic study of optimizing symbol legibility via a limited displacement of the symbols.
Specifically, we consider unit square symbols that need to be placed at specified y-coordinates. We optimize the drawing order of the symbols as well as their x-displacement, constrained within a rectangular container, to maximize the minimum visible perimeter over all squares. If the container has width and height at most 2, there is a point that stabs all squares. In this case, we prove that a staircase layout is arbitrarily close to optimality and can be computed in O(nlog n) time. If the width is at most 2, there is a vertical line that stabs all squares, and in this case, we give a 2-approximation algorithm (assuming fixed container height) that runs in O(nlog n) time. As a minimum visible perimeter of 2 is always trivially achievable, we measure this approximation with respect to the visible perimeter exceeding 2. We show that, despite its simplicity, the algorithm gives asymptotically optimal results for certain instances.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol294-swat2024/LIPIcs.SWAT.2024.24/LIPIcs.SWAT.2024.24.pdf
symbol placement
visibility
jittering
stacking order