The Power of Subsampling in Submodular Maximization

Christopher Harshaw, Ehsan Kazemi, Moran Feldman, Amin Karbasi

Research output: Contribution to journalArticlepeer-review


We propose subsampling as a unified algorithmic technique for submodular maximization in centralized and online settings. The idea is simple: independently sample elements from the ground set and use simple combinatorial techniques (such as greedy or local search) on these sampled elements. We show that this approach leads to optimal/state-of-the-art results despite being much simpler than existing methods. In the usual off-line setting, we present SAMPLEGREEDY, which obtains a (p + 2 + o(1))-approximation for maximizing a submodular function subject to a p-extendible system using O(n + nk=p) evaluation and feasibility queries, where k is the size of the largest feasible set. The approximation ratio improves to p + 1 and p for monotone submodular and linear objectives, respectively. In the streaming setting, we present SAMPLE-STREAMING, which obtains a (4p + 2 − o(1))-approximation for maximizing a submodular function subject to a p-matchoid using O(k) memory and O(km=p) evaluation and feasibility queries per element, and m is the number of matroids defining the p-matchoid. The approximation ratio improves to 4p for monotone submodular objectives. We empirically demonstrate the effectiveness of our algorithms on video summarization, location summarization, and movie recommendation tasks.

Original languageEnglish
Article number2
Pages (from-to)1365-1393
Number of pages29
JournalMathematics of Operations Research
Issue number2
Early online date13 Oct 2021
StatePublished - May 2022
Externally publishedYes

Bibliographical note

Funding Information:
Funding: This work was supported in part by a National Science Foundation (NSF) Graduate Research Fellowship [Grant DGE1122492] awarded to C. Harshaw, an Israel Science Foundation (ISF) [Grant 1357/16] awarded to M. Feldman, and the NSF [Grant IIS-1845032], the Office of Naval Research [Grant N00014-19-2406], and funding from TATA Sons Private Limited awarded to A. Karbasi.

Publisher Copyright:
© 2021 INFORMS


  • approximation algorithms
  • p-extendible systems
  • p-matchoids
  • streaming algorithms
  • submodular maximization
  • subsampling


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