Computing Stable Demers Cartograms

TL;DR

This paper introduces a linear programming method to compute stable Demers cartograms that preserve adjacencies and stability across multiple data representations, enhancing map visualization consistency.

Contribution

It presents a novel linear programming approach for generating stable Demers cartograms that maintain adjacency and positional stability across different data states.

Findings

Method guarantees most adjacencies are maintained with minimal leaders.

Experiments demonstrate good quality and stability of the generated cartograms.

Approach effectively balances adjacency preservation and stability across datasets.

Abstract

Cartograms are popular for visualizing numerical data for map regions. Maintaining correct adjacencies is a primary quality criterion for cartograms. When there are multiple data values per region (over time or different datasets) shown as animated or juxtaposed cartograms, preserving the viewer's mental-map in terms of stability between cartograms is another important criterion. We present a method to compute stable Demers cartograms, where each region is shown as a square and similar data yield similar cartograms. We enforce orthogonal separation constraints with linear programming, and measure quality in terms of keeping adjacent regions close (cartogram quality) and using similar positions for a region between the different data values (stability). Our method guarantees ability to connect most lost adjacencies with minimal leaders. Experiments show our method yields good quality and stability.