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MosaicSets: Embedding Set Systems into Grid Graphs.

Peter Rottmann, Markus Wallinger, Annika Bonerath

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    This summary is machine-generated.

    MosaicSets visualizes complex set systems using grid-based layouts, ensuring contiguous regions for each set. This novel approach optimizes compactness and handles NP-hard problems efficiently for real-world data.

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    Area of Science:

    • Information Visualization
    • Computational Geometry
    • Operations Research

    Background:

    • Visualizing relationships between sets is crucial in information visualization.
    • Existing methods struggle with non-spatial set systems and contiguity constraints.
    • Representing complex set structures requires novel algorithmic approaches.

    Purpose of the Study:

    • Introduce MosaicSets, a new method for creating Euler-like diagrams from non-spatial set systems.
    • Map elements to grid cells (hexagonal or square) ensuring set contiguity.
    • Optimize overall and individual set compactness while handling NP-hard computational challenges.

    Main Methods:

    • Integer linear programming to find optimal element-to-grid-cell assignments.
    • Relaxation of contiguity constraints for non-embeddable set systems.
    • Case study using university faculty research groups, departments, and projects.

    Main Results:

    • Demonstrated the NP-hard nature of the optimal mapping problem.
    • Integer linear programming effectively solves real-world instances rapidly.
    • Developed rendering styles and evaluated performance with quantitative measures and expert interviews.

    Conclusions:

    • MosaicSets provides an effective solution for visualizing complex set systems with contiguity requirements.
    • The integer linear programming approach offers optimal solutions for practical applications.
    • Relaxation techniques enhance the method's applicability to challenging set visualizations.