Generalized budgeted submodular set function maximization

• Published in: Information and computation Vol. 281; p. 104741
• Main Authors: Cellinese, Francesco, D'Angelo, Gianlorenzo, Monaco, Gianpiero, Velaj, Yllka
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2021
• Subjects: Approximation algorithms; Budgeted maximum coverage; Submodular set function; Approximation algorithms; Submodular set function; Budgeted maximum coverage
• ISSN: 0890-5401; 1090-2651
• DOI: 10.1016/j.ic.2021.104741

In the generalized budgeted submodular set function maximization problem, we are given a ground set of elements and a set of bins. Each bin has its own cost and the cost of each element depends on its associated bin. The goal is to find a subset of elements along with an associated set of bins such that the overall costs of both is at most a given budget, and the profit is maximized. We present an algorithm that guarantees a 12(1−1eα)-approximation, where α≤1 is the approximation factor of an algorithm for a sub-problem. If the costs satisfy a specific condition, we provide a polynomial-time algorithm that gives us α=1−ϵ, while for the general case we design an algorithm with α=1−1e−ϵ. We extend our results providing a bi-criterion approximation algorithm where we can spend an extra budget up to a factor β≥1 to guarantee a 12(1−1eαβ)-approximation.