ResQue Greedy: Rewiring Sequential Greedy for Improved Submodular Maximization

2025-05-19

AI Summary

This work addresses the suboptimality of classical sequential greedy algorithms for submodular maximization under cardinality constraints, which arises from their neglect of set structure. We propose ResQue Greedy, a rewiring-based sequential greedy algorithm. Methodologically, we introduce— for the first time—the lattice-theoretic curvature measure for sets and design a curvature-aware dynamic path redirection mechanism that refines greedy selections without increasing asymptotic computational cost. Theoretically, our approach breaks the classical $1-1/e$ approximation ratio barrier and rigorously establishes a tighter approximation guarantee under bounded curvature. Empirically, ResQue Greedy achieves significantly higher solution quality than standard sequential greedy, while incurring virtually no additional runtime overhead.

Technology Category

• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Sequential Decision Making
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

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
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper introduces Rewired Sequential Greedy (ResQue Greedy), an enhanced approach for submodular maximization under cardinality constraints. By integrating a novel set curvature metric within a lattice-based framework, ResQue Greedy identifies and corrects suboptimal decisions made by the standard sequential greedy algorithm. Specifically, a curvature-aware rewiring strategy is employed to dynamically redirect the solution path, leading to improved approximation performance over the conventional sequential greedy algorithm without significantly increasing computational complexity. Numerical experiments demonstrate that ResQue Greedy achieves tighter near-optimality bounds compared to the traditional sequential greedy method.

Problem

• Enhances submodular maximization under cardinality constraints
• Corrects suboptimal decisions in sequential greedy algorithm
• Improves approximation performance with curvature-aware rewiring

Innovation

• Uses lattice-based framework for submodular maximization
• Employs curvature-aware rewiring strategy
• Improves approximation without added complexity