[Paper Review] Exploring Algorithmic Fairness in Robust Graph Covering Problems

Aida Rahmattalabi, Phebe Vayanos+5 more|arXiv (Cornell University)|Jun 11, 2020

Vehicle Routing Optimization Methods32 citations

TL;DR

The paper introduces a robust graph covering framework with group fairness constraints, analyzes the price of fairness, and demonstrates a tractable approximation (K-ad adaptability) solved via MILP and Benders decomposition, validated on real-world social networks.

ABSTRACT

Fueled by algorithmic advances, AI algorithms are increasingly being deployed in settings subject to unanticipated challenges with complex social effects. Motivated by real-world deployment of AI driven, social-network based suicide prevention and landslide risk management interventions, this paper focuses on robust graph covering problems subject to group fairness constraints. We show that, in the absence of fairness constraints, state-of-the-art algorithms for the robust graph covering problem result in biased node coverage: they tend to discriminate individuals (nodes) based on membership in traditionally marginalized groups. To mitigate this issue, we propose a novel formulation of the robust graph covering problem with group fairness constraints and a tractable approximation scheme applicable to real-world instances. We provide a formal analysis of the price of group fairness (PoF) for this problem, where we show that uncertainty can lead to greater PoF. We demonstrate the effectiveness of our approach on several real-world social networks. Our method yields competitive node coverage while significantly improving group fairness relative to state-of-the-art methods.

Motivation & Objective

• Motivate robust graph covering in open-world social intervention contexts where monitor availability is uncertain.
• Mitigate discriminatory coverage across protected groups by embedding maximin group fairness constraints.
• Develop a tractable approximation for the fairness-constrained robust problem and analyze its computational properties.
• Quantify the price of group fairness under uncertainty and provide practical guidance for real networks.

Proposed method

• Formulate robust graph covering as a two-stage problem with decision variables for monitor selection and node coverage.
• Introduce maximin group fairness constraints ensuring a minimum fraction W of each group is covered under worst-case failures.
• Reformulate as a K-ad adaptability counterpart to obtain a linear (MILP) formulation that balances tractability and optimality.
• Apply Benders decomposition with symmetry-breaking to solve practical problem sizes.
• Derive an MILP reformulation that handles general upward-closed uncertainty sets and preserves fairness constraints.
• Provide analytical bounds on the price of group fairness under stochastic block model networks.

Experimental results

Research questions

• RQ1 How does enforcing group fairness affect worst-case coverage in robust graph covering under node failures?
• RQ2 What is the price of fairness (PoF) in deterministic and uncertain network settings, particularly in SBM networks?
• RQ3 Can we obtain a tractable, near-optimal solution for the fairness-constrained robust problem, and how does K-ad adaptability perform?
• RQ4 How do real-world social networks respond to fairness-constrained monitor placement compared to state-of-the-art methods?

Key findings

• Without fairness constraints, algorithms can cause significant racial disparity in coverage across real networks.
• A fairness-constrained formulation achieves max-min group fairness by ensuring a fraction W of each group is covered in the worst case.
• A K-adaptability MILP approximation improves solution quality over a single-scenario approach while remaining tractable for moderate K (best gains from K=2 or 3).
• Benders decomposition with symmetry-breaking enables solving practical problem sizes efficiently.
• In stochastic block model networks, the PoF bounds show how fairness constraints influence coverage, with PoF increasing with group imbalances and failure rates.
• Empirical results on five real homeless-youth networks show competitive overall coverage with substantially improved group fairness compared to prior methods.