Streaming Submodular Maximization under a k-Set System Constraint

Ran Haba, Ehsan Kazemi, Moran Feldman, Amin Karbasi
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:3939-3949, 2020.

Abstract

In this paper, we propose a novel framework that converts streaming algorithms for monotone submodular maximization into streaming algorithms for non-monotone submodular maximization. This reduction readily leads to the currently tightest deterministic approximation ratio for submodular maximization subject to a $k$-matchoid constraint. Moreover, we propose the first streaming algorithm for monotone submodular maximization subject to $k$-extendible and $k$-set system constraints. Together with our proposed reduction, we obtain $O(k\log k)$ and $O(k^2\log k)$ approximation ratio for submodular maximization subject to the above constraints, respectively. We extensively evaluate the empirical performance of our algorithm against the existing work in a series of experiments including finding the maximum independent set in randomly generated graphs, maximizing linear functions over social networks, movie recommendation, Yelp location summarization, and Twitter data summarization.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-haba20a, title = {Streaming Submodular Maximization under a k-Set System Constraint}, author = {Haba, Ran and Kazemi, Ehsan and Feldman, Moran and Karbasi, Amin}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {3939--3949}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/haba20a/haba20a.pdf}, url = {https://proceedings.mlr.press/v119/haba20a.html}, abstract = {In this paper, we propose a novel framework that converts streaming algorithms for monotone submodular maximization into streaming algorithms for non-monotone submodular maximization. This reduction readily leads to the currently tightest deterministic approximation ratio for submodular maximization subject to a $k$-matchoid constraint. Moreover, we propose the first streaming algorithm for monotone submodular maximization subject to $k$-extendible and $k$-set system constraints. Together with our proposed reduction, we obtain $O(k\log k)$ and $O(k^2\log k)$ approximation ratio for submodular maximization subject to the above constraints, respectively. We extensively evaluate the empirical performance of our algorithm against the existing work in a series of experiments including finding the maximum independent set in randomly generated graphs, maximizing linear functions over social networks, movie recommendation, Yelp location summarization, and Twitter data summarization.} }
Endnote
%0 Conference Paper %T Streaming Submodular Maximization under a k-Set System Constraint %A Ran Haba %A Ehsan Kazemi %A Moran Feldman %A Amin Karbasi %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-haba20a %I PMLR %P 3939--3949 %U https://proceedings.mlr.press/v119/haba20a.html %V 119 %X In this paper, we propose a novel framework that converts streaming algorithms for monotone submodular maximization into streaming algorithms for non-monotone submodular maximization. This reduction readily leads to the currently tightest deterministic approximation ratio for submodular maximization subject to a $k$-matchoid constraint. Moreover, we propose the first streaming algorithm for monotone submodular maximization subject to $k$-extendible and $k$-set system constraints. Together with our proposed reduction, we obtain $O(k\log k)$ and $O(k^2\log k)$ approximation ratio for submodular maximization subject to the above constraints, respectively. We extensively evaluate the empirical performance of our algorithm against the existing work in a series of experiments including finding the maximum independent set in randomly generated graphs, maximizing linear functions over social networks, movie recommendation, Yelp location summarization, and Twitter data summarization.
APA
Haba, R., Kazemi, E., Feldman, M. & Karbasi, A.. (2020). Streaming Submodular Maximization under a k-Set System Constraint. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:3939-3949 Available from https://proceedings.mlr.press/v119/haba20a.html.

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