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Submodular Streaming in All Its Glory: Tight Approximation, Minimum Memory and Low Adaptive Complexity
Ehsan Kazemi · Marko Mitrovic · Morteza Zadimoghaddam · Silvio Lattanzi · Amin Karbasi

Wed Jun 12 06:30 PM -- 09:00 PM (PDT) @ Pacific Ballroom #169
Streaming algorithms are generally judged by the quality of their solution, memory footprint, and computational complexity. In this paper, we study the problem of maximizing a monotone submodular function in the streaming setting with a cardinality constraint $k$. We first propose SIEVE-STREAMING++, which requires just one pass over the data, keeps only $O(k)$ elements and achieves the tight $\frac{1}{2}$-approximation guarantee. The best previously known streaming algorithms either achieve a suboptimal $\frac{1}{4}$-approximation with $\Theta(k)$ memory or the optimal $\frac{1}{2}$-approximation with $O(k\log k)$ memory. Next, we show that by buffering a small fraction of the stream and applying a careful filtering procedure, one can heavily reduce the number of adaptive computational rounds, thus substantially lowering the computational complexity of SIEVE-STREAMING++. We then generalize our results to the more challenging multi-source streaming setting. We show how one can achieve the tight $\frac{1}{2}$-approximation guarantee with $O(k)$ shared memory, while minimizing not only the rounds of computations but also the total number of communicated bits. Finally, we demonstrate the efficiency of our algorithms on real-world data summarization tasks for multi-source streams of tweets and of YouTube videos.

Author Information

Ehsan Kazemi (Yale)
Marko Mitrovic (Yale University)
Morteza Zadimoghaddam (Google)
Silvio Lattanzi (Google Zurich)
Amin Karbasi (Yale)
Amin Karbasi

Amin Karbasi is currently an assistant professor of Electrical Engineering, Computer Science, and Statistics at Yale University. He has been the recipient of the National Science Foundation (NSF) Career Award 2019, Office of Naval Research (ONR) Young Investigator Award 2019, Air Force Office of Scientific Research (AFOSR) Young Investigator Award 2018, DARPA Young Faculty Award 2016, National Academy of Engineering Grainger Award 2017, Amazon Research Award 2018, Google Faculty Research Award 2016, Microsoft Azure Research Award 2016, Simons Research Fellowship 2017, and ETH Research Fellowship 2013. His work has also been recognized with a number of paper awards, including Medical Image Computing and Computer Assisted Interventions Conference (MICCAI) 2017, International Conference on Artificial Intelligence and Statistics (AISTAT) 2015, IEEE ComSoc Data Storage 2013, International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 2011, ACM SIGMETRICS 2010, and IEEE International Symposium on Information Theory (ISIT) 2010 (runner-up). His Ph.D. thesis received the Patrick Denantes Memorial Prize 2013 from the School of Computer and Communication Sciences at EPFL, Switzerland.

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