Cardinality constrained submodular maximization for random streamsDownload PDF

May 21, 2021 (edited Oct 26, 2021)NeurIPS 2021 PosterReaders: Everyone
  • Keywords: submodular, streaming model, optimization, cardinality constraint, approximation algorithms
  • TL;DR: We give $(1-1/e-\varepsilon)$ and $1/e-\varepsilon$ approximations for submodular maximization under a cardinality constraint in $O(k/\varepsilon)$ memory.
  • Abstract: We consider the problem of maximizing submodular functions in single-pass streaming and secretaries-with-shortlists models, both with random arrival order. For cardinality constrained monotone functions, Agrawal, Shadravan, and Stein~\cite{SMC19} gave a single-pass $(1-1/e-\varepsilon)$-approximation algorithm using only linear memory, but their exponential dependence on $\varepsilon$ makes it impractical even for $\varepsilon=0.1$. We simplify both the algorithm and the analysis, obtaining an exponential improvement in the $\varepsilon$-dependence (in particular, $O(k/\varepsilon)$ memory). Extending these techniques, we also give a simple $(1/e-\varepsilon)$-approximation for non-monotone functions in $O(k/\varepsilon)$ memory. For the monotone case, we also give a corresponding unconditional hardness barrier of $1-1/e+\varepsilon$ for single-pass algorithms in randomly ordered streams, even assuming unlimited computation. Finally, we show that the algorithms are simple to implement and work well on real world datasets.
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