Two-stage submodular maximization problem beyond nonnegative and monotone

We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximatio...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical structures in computer science Vol. 34; no. 3; pp. 211 - 226
Main Authors: Liu, Zhicheng, Chang, Hong, Ma, Ran, Du, Donglei, Zhang, Xiaoyan
Format: Journal Article
Language:English
Published: 01.03.2024
ISSN:0960-1295, 1469-8072
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximation algorithms for this problem. The first is a deterministic $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}} \right),1} \right)$ -approximation algorithm, and the second is a randomized $\left( {{1 \over {k + 1}}\left( {1 - {1 \over {{e^{k + 1}}} \right) - \varepsilon ,1} \right)$ -approximation algorithm with improved time efficiency.
ISSN:0960-1295
1469-8072
DOI:10.1017/S0960129521000372