Two-stage submodular maximization problem beyond nonnegative and monotone

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Mathematical Structures in Computer Science Pub Date : 2021-11-16 DOI:10.1017/s0960129521000372

Zhicheng Liu, Hong Chang, Ran Ma, D. Du, Xiaoyan Zhang

引用次数: 0

Abstract

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.

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超越非负单调的两阶段子模最大化问题

我们考虑一个受基数约束和k拟阵约束的两阶段子模最大化问题，其中目标函数是非负单调子模函数和非负单调模函数的期望差。针对这个问题，我们给出了两种双因子近似算法。第一种是确定性$\left（｛｛1\over{k+1｝｝\left（｛1-｛1\over｛e^｛k+1｝｝\right），1｝\right）$-近似算法，第二种是具有改进的时间效率的随机$\lefort（｛1\over{k+1}｝\left（｛1-{1\over{e^｛k+1｝}\right）-\varepsilon，1｝\right）$-逼近算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Structures in Computer Science 工程技术-计算机：理论方法

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.