We study the problem of maximizing a non-monotone submodular function subject to a cardinality constraint in the streaming model. Our main contributions are two single-pass (semi-)streaming algorithms that use Õ(k) · poly(1/ε) memory, where k is the size constraint. At the end of the stream, both our algorithms post-process their data structures using any offline algorithm for submodular maximization, and obtain a solution whose approximation guarantee is 1+αα − ε, where α is the approximation of the offline algorithm. If we use an exact (exponential time) post-processing algorithm, this leads to 12 − ε approximation (which is nearly optimal). If we post-process with the algorithm of , that achieves the state-of-the-art offline approximation guarantee of α = 0.385, we obtain 0.2779-approximation in polynomial time, improving over the previously best polynomial-time approximation of 0.1715 due to . One of our algorithms is combinatorial and enjoys fast update and overall running times. Our other algorithm is based on the multilinear extension, enjoys an improved space complexity, and can be made deterministic in some settings of interest.
|Title of host publication||47th International Colloquium on Automata, Languages, and Programming, ICALP 2020|
|Editors||Artur Czumaj, Anuj Dawar, Emanuela Merelli|
|Publisher||Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing|
|State||Published - 1 Jun 2020|
|Event||47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 - Virtual, Online, Germany|
Duration: 8 Jul 2020 → 11 Jul 2020
|Name||Leibniz International Proceedings in Informatics, LIPIcs|
|Conference||47th International Colloquium on Automata, Languages, and Programming, ICALP 2020|
|Period||8/07/20 → 11/07/20|
Bibliographical noteFunding Information:
Funding Naor Alaluf : The work of Naor Alaluf was supported in part by ISF grant number 1357/16. Alina Ene: The work of Alina Ene was supported in part by NSF CAREER grant CCF-1750333, NSF grant CCF-1718342, and NSF grant III-1908510. Moran Feldman: The work of Moran Feldman was supported in part by ISF grant number 1357/16. Huy L. Nguyen: The work of Huy L. Nguyen was supported in part by NSF CAREER grant CCF-1750716 and NSF grant CCF-1909314. Andrew Suh: The work of Andrew Suh was supported in part by NSF CAREER grant CCF-1750333, NSF grant CCF-1718342, and NSF grant III-1908510.
© Naor Alaluf, Alina Ene, Moran Feldman, Huy L. Nguyen, and Andrew Suh; licensed under Creative Commons License CC-BY 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020).
- Cardinality constraint
- Streaming algorithms
- Submodular maximization
ASJC Scopus subject areas