Bicriteria Algorithms for Submodular Cover with Partition and Fairness Constraints

2026-01-16

AI Summary

This work addresses a key limitation in submodular cover problems—the neglect of natural data partitioning—by systematically studying, for the first time, an NP-hard variant that incorporates both partition and fairness constraints. To tackle this challenge, the authors propose a scalable bicriteria approximation algorithm applicable to both monotone and non-monotone objective functions. The method achieves a theoretically optimal approximation ratio while substantially reducing query complexity. It simultaneously ensures high-quality coverage and fairness across partitions, striking a balance between utility and equitable representation. Extensive experiments on both real-world and synthetic datasets demonstrate the algorithm’s efficiency and effectiveness, confirming its practical viability for large-scale, structured data scenarios.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Non-convex Optimization
• Game Theory and Economic Paradigms: Fair Division

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

In many submodular optimization applications, datasets are naturally partitioned into disjoint subsets. These scenarios give rise to submodular optimization problems with partition-based constraints, where the desired solution set should be in some sense balanced, fair, or resource-constrained across these partitions. While existing work on submodular cover largely overlooks this structure, we initiate a comprehensive study of the problem of Submodular Cover with Partition Constraints (SCP) and its key variants. Our main contributions are the development and analysis of scalable bicriteria approximation algorithms for these NP-hard optimization problems for both monotone and nonmonotone objectives. Notably, the algorithms proposed for the monotone case achieve optimal approximation guarantees while significantly reducing query complexity compared to existing methods. Finally, empirical evaluations on real-world and synthetic datasets further validate the efficiency and effectiveness of the proposed algorithms.

Problem

• Submodular Cover
• Partition Constraints
• Fairness Constraints
• Bicriteria Optimization
• NP-hard Optimization

Innovation

• submodular cover
• partition constraints
• bicriteria approximation
• query complexity
• fairness constraints