We study streaming submodular maximization subject to matching/b-matching constraints (MSM/MSbM), and present improved upper and lower bounds for these problems. On the upper bounds front, we give primaldual algorithms achieving the following approximation ratios.
for monotone MSM, improving the previous best ratio of 7.75.
for non-monotone MSM, improving the previous best ratio of 9.899.
for maximum weight b-matching, improving the previous best ratio of 4 + ∊.
On the lower bounds front, we improve on the previous best lower bound of for MSM, and show ETH-based lower bounds of ≈ 1.914 for polytime monotone MSM streaming algorithms.
Our most substantial contributions are our algorithmic techniques. We show that the (randomized) primal-dual method, which originated in the study of maximum weight matching (MWM), is also useful in the context of MSM. To our knowledge, this is the first use of primal-dual based analysis for streaming submodular optimization. We also show how to reinterpret previous algorithms for MSM in our framework; hence, we hope our work is a step towards unifying old and new techniques for streaming submodular maximization, and that it paves the way for further new results.

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cover image Proceedings
Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA)
Pages: 1914 - 1933
Editor: Dániel Marx, CISPA Helmholtz Center for Information Security, Germany
ISBN (Online): 978-1-61197-646-5


Published online: 7 January 2021



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