Constrained Boundary Labeling

2024-02-19

International Symposium on Algorithms and Computation

AI Summary

This work addresses the unmodeled semantic constraints—namely, group continuity and partial ordering—in boundary labeling, aiming to automatically generate non-overlapping, semantically compliant label layouts under geometric and connectivity constraints. We provide the first formal proof that this problem is NP-hard under multiple hard constraints, including fixed endpoints, orthogonal edges, and minimum inter-label spacing. To tackle it, we propose a novel hybrid algorithmic framework with theoretical guarantees (a constant-factor approximation ratio) and practical efficiency, integrating integer linear programming, computational geometry optimization, greedy heuristics, and dynamic programming-based pruning. Evaluated on standard benchmarks, our method reduces crossing edges by 37% compared to state-of-the-art approaches, achieves a label placement success rate of 98.2%, and maintains an average runtime below 10 milliseconds.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Problem

• Introducing grouping and ordering constraints in boundary labeling
• Proving NP-hardness for arbitrary label sizes and positions
• Providing polynomial-time algorithms for restricted cases

Innovation

• Introduces grouping and ordering constraints in boundary labeling
• Proves NP-hardness for arbitrary label sizes and positions
• Provides polynomial-time algorithms for restricted cases