Streaming submodular matching meets the primal-dual method

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 primal-dual algorithms achieving the following approximation ratios. • 3 + 2√2 ≈ 5.828 for monotone MSM, improving the previous best ratio of 7.75. • 4 + 3√2 ≈ 7.464 for non-monotone MSM, improving the previous best ratio of 9.899. • 3 + ε for maximum weight b-matching, improving the previous best ratio of 4 + ε. On the lower bounds front, we improve on the previous e best lower bound of ≈ 1.582 for MSM, and e−1 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.