On Maximizing the Difference Between an Approximately Submodular Function and a Linear Function Subject to a Matroid Constraint

• Published in: Combinatorial Optimization and Applications Vol. 13135; pp. 75 - 85
• Main Authors: Wang, Yijing, Xu, Yicheng, Yang, Xiaoguang
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2021; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Approximately submodular; Bicriteria algorithm; Massive data; Matroid constraint
• ISBN: 9783030926809; 303092680X
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-92681-6_7

In this paper, we investigate the problem of maximizing the difference between an approximately submodular function and a non-negative linear function subject to a matroid constraint. This model has widespread applications in real life, such as the team formation problem in labor market and the assortment optimization in sales market. We provide a bicriteria approximation algorithm with bifactor ratio (γ1+γ,1) $$(\frac{\gamma }{1+\gamma },1)$$ , where γ∈(0,1] $$\gamma \in (0,1]$$ is a parameter to characterize the approximate submodularity. Our result extends Ene’s recent work on maximizing the difference between a monotone submodular function and a linear function. Also, a generalized version of the proposed algorithm is capable to deal with huge volume data set.