Generalized budgeted submodular set function maximization

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...

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Bibliographic Details
Published inInformation and computation Vol. 281; p. 104741
Main Authors Cellinese, Francesco, D'Angelo, Gianlorenzo, Monaco, Gianpiero, Velaj, Yllka
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2021
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ISSN0890-5401
1090-2651
DOI10.1016/j.ic.2021.104741

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Summary: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.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2021.104741