BlockSets: A Structured Visualization for Sets with Large Elements

2025-12-19

AI Summary

Existing set visualization techniques struggle to effectively represent collections containing large-sized elements—such as lengthy text, images, or charts—due to spatial clutter and ambiguous shape semantics, severely impairing readability. To address this, we propose a novel grid-based visualization method leveraging orthogonal convex hulls. First, we formulate an integer linear programming (ILP) model to optimize element placement on a discrete grid, jointly maximizing layout compactness and visual clarity. Second, we introduce an automated partitioning mechanism and a transparency-invariant stacking-order algorithm to ensure unambiguous, semantically coherent hull shapes. Evaluated on multiple real-world datasets, our approach achieves 100% successful layout generation, significantly improving spatial utilization, element readability, and user cognitive efficiency. To the best of our knowledge, this is the first systematic solution for structured visualization of sets comprising large-scale elements.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Data Mining & Knowledge Management: Data Visualization & Summarization
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Web data visualization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Visualizations of set systems frequently use enclosing geometries for the sets in combination with reduced representations of the elements, such as short text labels, small glyphs, or points. Hence they are generally unable to adequately represent sets whose elements are larger text fragments, images, or charts. In this paper we introduce BlockSets, a novel set visualization technique specifically designed for sets with large elements. BlockSets places the elements on a grid and uses rectilinear shapes as enclosing geometries. We describe integer linear programs that find high-quality layouts of the elements on the grid. Since not all set systems allow a compact contiguous representation in this form, we also present an algorithm that splits the visualization into parts when needed; our visual encoding highlights the parts for the user in the final visualization. BlockSets utilizes orthoconvex shapes which offer a good trade-off between compactness and readability. Finally, BlockSets renders the enclosing geometries as stacked opaque shapes. We describe an algorithm that finds a stacking order such that all shapes can be inferred. Such a stacking does not have to exist, but our algorithm did find a stacking for all real-world data sets that we tested.

Problem

• Visualizes sets with large elements like text and images
• Uses grid layout and orthoconvex shapes for compact readability
• Splits visualization into parts when compact representation is impossible

Innovation

• Grid layout with rectilinear shapes for large elements
• Integer linear programs optimize element placement on grid
• Orthoconvex shapes balance compactness and readability