When Weak Submodularity Meets Matroids: How Does Standard Greedy Behave?
Weakly submodular maximization finds numerous applications in machine learning, data mining and statistics. In particular, under a cardinality constraint, the standard greedy algorithm is known to attain the tight $(1-e^{-γ})$-approximation guarantee, where $γ$ denotes the submodularity ratio. However, when considering general matroid constraints, \emph{how well standard greedy can perform} has remained a longstanding open question. In this paper, we resolve this question by studying the worst-case approximation guarantee $R_{\mathrm{gr}}(γ,r)$ of standard forward greedy, where $r$ is the rank of matroid. Specifically, our first contribution is the following refined lower bound \begin{equ...
| Authors | Qixin Zhang, Shi Fu, Shengminjie Chen et al. |
|---|---|
| Primary category | math.OC |
| Published | 18 October 2026 |
| Last updated at source | 21 October 2026 |
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