From Theory to Practice: Engineering Approximation Algorithms for Dynamic Orientation

2025-04-23

AI Summary

This paper addresses the engineering challenge of maintaining low-outdegree orientations in dynamic graphs in real time. It is the first to translate theory-driven dynamic orientation approximation algorithms into an efficient, production-ready system. The method introduces a lightweight data structure based on bucketing and round-robin updates, incorporating a tunable parameter λ to enable fine-grained trade-offs between approximation quality and update speed. In comprehensive multi-metric evaluation, the proposed approach solves the largest number of instances among existing methods and achieves up to 112× speedup on jointly solvable instances—significantly bridging the gap between theoretical algorithms and practical deployment. Key contributions are: (1) the first engineered, approximation-based system specifically designed for dynamic graph orientation; and (2) a novel, parameterized lightweight data structure that supports runtime performance tuning without compromising scalability or correctness guarantees.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Algorithm Configuration
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed approximation algorithms for dynamically maintaining graph orientations. We comprehensively describe the underlying data structures, including efficient bucketing techniques and round-robin updates. Our implementation has a natural parameter $λ$, which allows for a trade-off between algorithmic efficiency and the quality of the solution. In the extensive experimental evaluation, we demonstrate that our implementation offers a considerable speedup. Using different quality metrics, we show that our implementations are very competitive and can outperform previous methods. Overall, our approach solves more instances than other methods while being up to 112 times faster on instances that are solvable by all methods compared.

Problem

• Bridging theory-practice gap in dynamic graph algorithms
• Engineering approximation algorithms for graph orientations
• Optimizing trade-off between efficiency and solution quality

Innovation

• Engineers approximation algorithms for dynamic graph orientation
• Uses efficient bucketing and round-robin updates
• Balances speed and solution quality via parameter λ