Multicriteria Optimization for Dynamic Demers Cartograms.

Area of Science:

• Computational Geometry
• Data Visualization
• Geographic Information Systems

Background:

• Cartograms are widely used for visualizing data across administrative regions.
• Maintaining viewer stability between multiple cartograms (e.g., animated or juxtaposed) is crucial, alongside traditional criteria like adjacency preservation.
• Existing methods may not adequately ensure stability when displaying multiple data values for the same regions.

Purpose of the Study:

• To develop a method for computing stable Demers cartograms that preserve visual consistency across different datasets.
• To ensure that similar data inputs result in similar cartogram outputs, enhancing viewer comprehension.
• To balance traditional cartogram quality (e.g., adjacency) with the new criterion of temporal or cross-dataset stability.

Main Methods:

• The method computes Demers cartograms where each region is represented by a square scaled to its data value.
• Orthogonal separation constraints are enforced using linear programming.
• Quality is measured by adjacency preservation (cartogram quality) and positional consistency across datasets (stability).

Main Results:

• The proposed method generates stable Demers cartograms.
• It ensures that similar data values lead to similar cartogram representations.
• The method guarantees the ability to reconnect most lost adjacencies using minimal-length planar orthogonal polylines.
• Experimental results demonstrate good performance across multiple quality and stability metrics.

Conclusions:

• The developed method effectively produces high-quality and stable Demers cartograms.
• This approach enhances the visualization of multiple data values by maintaining viewer stability.
• The technique offers a valuable tool for comparative analysis using animated or juxtaposed cartograms.