skip to main content


Title: Submodular Maximization with Nearly-optimal Approximation and Adaptivity in Nearly-linear Time
Award ID(s):
1750716
NSF-PAR ID:
10087830
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms
Page Range / eLocation ID:
274-282
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. In this paper, we study the tradeoff between the approximation guarantee and adaptivity for the problem of maximizing a monotone submodular function subject to a cardinality constraint. The adaptivity of an algorithm is the number of sequential rounds of queries it makes to the evaluation oracle of the function, where in every round the algorithm is allowed to make polynomially-many parallel queries. Adaptivity is an important consideration in settings where the objective function is estimated using samples and in applications where adaptivity is the main running time bottleneck. Previous algorithms achieving a nearly-optimal $1 - 1/e - \epsilon$ approximation require $\Omega(n)$ rounds of adaptivity. In this work, we give the first algorithm that achieves a $1 - 1/e - \epsilon$ approximation using $O(\ln{n} / \epsilon^2)$ rounds of adaptivity. The number of function evaluations and additional running time of the algorithm are $O(n \; \mathrm{poly}(\log{n}, 1/\epsilon))$. 
    more » « less
  2. null (Ed.)