ResQue Greedy: Rewiring Sequential Greedy for Improved Submodular Maximization

TL;DR

ResQue Greedy is a new algorithm that improves submodular maximization by dynamically rewiring decisions based on a set curvature metric, resulting in better approximation bounds.

Contribution

It introduces a curvature-aware rewiring strategy within a lattice framework to enhance the sequential greedy algorithm for submodular maximization.

Findings

Achieves tighter near-optimality bounds

Improves approximation performance over standard greedy

Maintains computational efficiency

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.