MosaicSets: Embedding Set Systems into Grid Graphs

TL;DR

MosaicSets introduces a method to visualize set systems as contiguous regions on grid graphs, optimizing layout compactness and contiguity, with practical applications demonstrated through real-world case studies.

Contribution

The paper presents a novel grid-based visualization technique for set systems, including an ILP-based optimization approach and a relaxation for non-embeddable sets.

Findings

Optimal mappings found efficiently for real-world data

Contiguity relaxation enables visualization of complex set systems

Qualitative and quantitative evaluation confirms effectiveness

Abstract

Visualizing sets of elements and their relations is an important research area in information visualization. In this paper, we present MosaicSets: a novel approach to create Euler-like diagrams from non-spatial set systems such that each element occupies one cell of a regular hexagonal or square grid. The main challenge is to find an assignment of the elements to the grid cells such that each set constitutes a contiguous region. As use case, we consider the research groups of a university faculty as elements, and the departments and joint research projects as sets. We aim at finding a suitable mapping between the research groups and the grid cells such that the department structure forms a base map layout. Our objectives are to optimize both the compactness of the entirety of all cells and of each set by itself. We show that computing the mapping is NP-hard. However, using integer linear programming we can solve real-world instances optimally within a few seconds. Moreover, we propose a relaxation of the contiguity requirement to visualize otherwise non-embeddable set systems. We present and discuss different rendering styles for the set overlays. Based on a case study with real-world data, our evaluation comprises quantitative measures as well as expert interviews.