Maximization of Approximately Submodular Functions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909393927274496 |
|---|---|
| author | Horel, Thibaut Singer, Yaron |
| author_facet | Horel, Thibaut Singer, Yaron |
| contents | We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a submodular function break submodularity. Say that $F$ is $\varepsilon$-approximately submodular if there exists a submodular function $f$ such that $(1-\varepsilon)f(S) \leq F(S)\leq (1+\varepsilon)f(S)$ for all subsets $S$. We are interested in characterizing the query-complexity of maximizing $F$ subject to a cardinality constraint $k$ as a function of the error level $\varepsilon>0$. We provide both lower and upper bounds: for $\varepsilon>n^{-1/2}$ we show an exponential query-complexity lower bound. In contrast, when $\varepsilon< {1}/{k}$ or under a stronger bounded curvature assumption, we give constant approximation algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10949 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximization of Approximately Submodular Functions Horel, Thibaut Singer, Yaron Data Structures and Algorithms Computational Complexity We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a submodular function break submodularity. Say that $F$ is $\varepsilon$-approximately submodular if there exists a submodular function $f$ such that $(1-\varepsilon)f(S) \leq F(S)\leq (1+\varepsilon)f(S)$ for all subsets $S$. We are interested in characterizing the query-complexity of maximizing $F$ subject to a cardinality constraint $k$ as a function of the error level $\varepsilon>0$. We provide both lower and upper bounds: for $\varepsilon>n^{-1/2}$ we show an exponential query-complexity lower bound. In contrast, when $\varepsilon< {1}/{k}$ or under a stronger bounded curvature assumption, we give constant approximation algorithms. |
| title | Maximization of Approximately Submodular Functions |
| topic | Data Structures and Algorithms Computational Complexity |
| url | https://arxiv.org/abs/2411.10949 |