Submodular Maximization in Exactly $n$ Queries
Abstract
In this work, we study the classical problem of maximizing a submodular function subject to a matroid constraint. We develop deterministic algorithms that are very parsimonious with respect to querying the submodular function, for both the case when the submodular function is monotone and the general submodular case. In particular, we present a 1/4 approximation algorithm for the monotone case that uses exactly one query per element, which gives the same total number of queries n as the number of queries required to compute the maximum singleton. For the general case, we present a constant factor approximation algorithm that requires 2 queries per element, which is the first algorithm for this problem with linear query complexity in the size of the ground set.
Cite
@article{arxiv.2406.00148,
title = {Submodular Maximization in Exactly $n$ Queries},
author = {Eric Balkanski and Steven DiSilvio and Alan Kuhnle and ChunLi Peng},
journal= {arXiv preprint arXiv:2406.00148},
year = {2024}
}
Comments
The same algorithm and 1/4 approximation result for the monotone case were previously obtained by Dutting et al. [14]. At the time of writing, we were not aware of this other paper. We generalize the algorithm to the p-matchoid constraints. Due to the base algorithm for the monotone case being identical as in Dutting et al. [14], we view the technical contribution of this manuscript limited