Generalized budgeted submodular set function maximization
Information and Computation(2021)
摘要
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.
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关键词
Submodular set function,Approximation algorithms,Budgeted maximum coverage
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