On Maximizing a Weakly Submodular Function over a Matroid Constraint via the Greedy Algorithm

2026-09-04

AI Summary

本文探讨了在一般拟阵约束下，使用贪婪算法最大化弱次模函数的问题，并证明了该方法无法提供常数近似解。

Abstract

We consider the problem of approximately maximizing a weakly submodular function using the standard greedy algorithm, which is known to give tight approximation results for such functions under a cardinality constraint. We show that this is not the case for general matroid constraints. For any $γ< 1$, we give a family of $γ$-weakly submodular functions and a simple partition matroid constraint and show that the standard greedy algorithm provides no constant approximation for the resulting constrained maximization problem.

Problem

• weakly submodular function
• matroid constraint
• greedy algorithm

Innovation

• weakly submodular function
• matroid constraint
• greedy algorithm
• approximation ratio