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On Minimizing Wiggle in Stacked Area Charts

Authors Alexander Dobler , Martin Nöllenburg

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LIPIcs.WADS.2025.22.pdf
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ACM Subject Classification
  • Mathematics of computing → Permutations and combinations
  • Theory of computation → Theory and algorithms for application domains
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Stacked area charts
  • NP-hardness
  • Mixed-integer linear programming

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Abstract

Stacked area charts are a widely used visualization technique for numerical time series. The x-axis represents time, and the time series are displayed as horizontal, variable-height layers stacked on top of each other. The height of each layer corresponds to the time series values at each time point. The main aesthetic criterion for optimizing the readability of stacked area charts is the amount of vertical change of the borders between the time series in the visualization, called wiggle. While many heuristic algorithms have been developed to minimize wiggle, the computational complexity of minimizing wiggle has not been formally analyzed. In this paper, we show that different variants of wiggle minimization are NP-hard and even hard to approximate. We also present an exact mixed-integer linear programming formulation and compare its performance with a state-of-the-art heuristic in an experimental evaluation. Lastly, we consider a special case of wiggle minimization that corresponds to the fundamentally interesting and natural problem of ordering a set of numbers as to minimize their sum of absolute prefix sums. We show several complexity results for this problem that imply some of the mentioned hardness results for wiggle minimization.

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Alexander Dobler and Martin Nöllenburg. On Minimizing Wiggle in Stacked Area Charts. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.22

Author Details

Alexander Dobler
  • TU Wien, Austria
Martin Nöllenburg
  • TU Wien, Austria

Funding

  • Dobler, Alexander: Supported by the Vienna Science and Technology Fund (WWTF) under grant [10.47379/ICT19035].
  • Nöllenburg, Martin: Supported by the Vienna Science and Technology Fund (WWTF) under grant [10.47379/ICT19035].

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References

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