LinSets.zip: Compressing Linear Set Diagrams

TL;DR

LinSets.zip introduces a novel space-efficient method for visualizing set systems with linear diagrams by reordering columns and allowing multiple sets per row, improving readability and reducing visual clutter.

Contribution

The paper presents LinSets.zip, a new approach that compresses linear diagrams through column reordering and row compression, with implementation via integer-linear programming and heuristics.

Findings

Reduces total gaps in linear diagrams

Allows multiple non-intersecting sets per row

Improves readability and space efficiency

Abstract

Linear diagrams are used to visualize set systems by depicting set memberships as horizontal line segments in a matrix, where each set is represented as a row and each element as a column. Each such line segment of a set is shown in a contiguous horizontal range of cells of the matrix indicating that the corresponding elements in the columns belong to the set. As each set occupies its own row in the matrix, the total height of the resulting visualization is as large as the number of sets in the instance. Such a linear diagram can be visually sparse and intersecting sets containing the same element might be represented by distant rows. To alleviate such undesirable effects, we present LinSets.zip, a new approach that achieves a more space-efficient representation of linear diagrams. First, we minimize the total number of gaps in the horizontal segments by reordering columns, a criterion that has been shown to increase readability in linear diagrams. The main difference of LinSets.zip to linear diagrams is that multiple non-intersecting sets can be positioned in the same row of the matrix. Furthermore, we present several different rendering variations for a matrix-based representation that utilize the proposed row compression. We implemented the different steps of our approach in a visualization pipeline using integer-linear programming, and suitable heuristics aiming at sufficiently fast computations in practice. We conducted both a quantitative evaluation and a small-scale user experiment to compare the effects of compressing linear diagrams.