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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Published in | Information and computation Vol. 281; p. 104741 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.12.2021
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Subjects | |
Online Access | Get full text |
ISSN | 0890-5401 1090-2651 |
DOI | 10.1016/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. |
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ISSN: | 0890-5401 1090-2651 |
DOI: | 10.1016/j.ic.2021.104741 |