Abstract
Submodular functions play a key role in combinatorial optimization field. The problem of maximizing submodular and non-submodular functions on the integer lattice has received a lot of recent attention. In this paper, we study streaming algorithms for the problem of maximizing a monotone non-submodular functions with cardinality constraint on the integer lattice. For a monotone non-submodular function \(f:\mathbf{Z} ^{n}_{+}\rightarrow \mathbf{R} _{+}\) defined on the integer lattice with diminishing-return (DR) ratio \(\gamma \), we present a one pass streaming algorithm that gives a \((1-\frac{1}{2^{\gamma }}-\epsilon )\)-approximation, requires at most \(O(k\epsilon ^{-1}\log {k/\gamma })\) space and \(O(\epsilon ^{-1}\log {k/\gamma }\cdot \) \(\log {\Vert \mathbf{B} \Vert _{\infty }})\) update time per element. To the best of our knowledge, this is the first streaming algorithm on the integer lattice for this constrained maximization problem.
This work was supported in part by the National Natural Science Foundation of China (11971447, 11871442), and the Fundamental Research Funds for the Central Universities.
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Liu, B., Chen, Z., Wang, H., Wu, W. (2021). Streaming Algorithms for Maximizing Non-submodular Functions on the Integer Lattice. 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_1
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