Fair Minimum Labeling: Efficient Temporal Network Activations for Reachability and Equity

2025-10-04

AI Summary

This paper studies the minimum-cost edge activation problem in temporal networks under group fairness constraints: given node groups and a target set, each group must reach the target within a specified time window, with fair allocation of reachability resources across groups. We formalize this as the Fair Minimum Labeling (FML) problem, prove its NP-hardness and establish a tight approximation lower bound. We design the first randomized algorithm achieving the theoretically optimal approximation ratio, integrating temporal reachability modeling, probabilistic approximation, and combinatorial optimization techniques. Experiments demonstrate that FML significantly reduces edge activation cost in applications such as distributed data aggregation, while strictly enforcing group-level fairness. To our knowledge, this is the first work to formally define and efficiently balance cost-efficiency and group fairness in temporal connectivity.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Active Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

Balancing resource efficiency and fairness is critical in networked systems that support modern learning applications. We introduce the Fair Minimum Labeling (FML) problem: the task of designing a minimum-cost temporal edge activation plan that ensures each group of nodes in a network has sufficient access to a designated target set, according to specified coverage requirements. FML captures key trade-offs in systems where edge activations incur resource costs and equitable access is essential, such as distributed data collection, update dissemination in edge-cloud systems, and fair service restoration in critical infrastructure. We show that FML is NP-hard and $Ω(log |V|)$-hard to approximate, and we present probabilistic approximation algorithms that match this bound, achieving the best possible guarantee for the activation cost. We demonstrate the practical utility of FML in a fair multi-source data aggregation task for training a shared model. Empirical results show that FML enforces group-level fairness with substantially lower activation cost than baseline heuristics, underscoring its potential for building resource-efficient, equitable temporal reachability in learning-integrated networks.

Problem

• Designing minimal-cost temporal edge activation plans for networks
• Ensuring equitable node group access to target sets
• Balancing resource efficiency with fairness in networked systems

Innovation

• Minimum-cost temporal edge activation plan
• Probabilistic approximation algorithms for NP-hard problem
• Enforcing group-level fairness with lower activation cost