Abstract
In recent years, submodularity has been found in a wide range of connections and applications with different scientific fields. However, many applications in practice do not fully meet the characteristics of diminishing returns. In this paper, we consider the problem of maximizing unconstrained non-negative weakly-monotone non-submodular set function. The generic submodularity ratio \(\gamma \) is a bridge connecting the non-negative monotone functions and the submodular functions, and no longer applicable to the non-monotone functions. We study a class of non-monotone functions, define as the weakly-monotone function, redefine the submodular ratio related to it and name it weakly-monotone submodularity ratio \(\widehat{\gamma }\), propose a deterministic double greedy algorithm, which implements the \(\frac{\widehat{\gamma }}{\widehat{\gamma }+2}\) approximation of the maximizing unconstrained non-negative weakly-monotone function problem. When \(\widehat{\gamma }=1\), the algorithm achieves an approximate guarantee of 1/3, achieving the same ratio as the deterministic algorithm for the unconstrained submodular maximization problem.
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Acknowledgements
The first and third authors are supported by National Natural Science Foundation of China (No. 12131003) and Beijing Natural Science Foundation Project No. Z200002. The second author is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant 06446, and Natural Science Foundation of China (Nos. 11771386, 11728104). The fourth author is supported by the Fundamental Research Funds for the Central Universities (No. E1E40108).
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Cui, M., Du, D., Xu, D., Yang, R. (2021). Approximation Algorithm for Maximizing Nonnegative Weakly Monotonic Set Functions. In: Mohaisen, D., Jin, R. (eds) Computational Data and Social Networks. CSoNet 2021. Lecture Notes in Computer Science(), vol 13116. Springer, Cham. https://doi.org/10.1007/978-3-030-91434-9_5
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DOI: https://doi.org/10.1007/978-3-030-91434-9_5
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