English

A Refined Analysis of Submodular Greedy

Data Structures and Algorithms 2021-03-16 v2

Abstract

Many algorithms for maximizing a monotone submodular function subject to a knapsack constraint rely on the natural greedy heuristic. We present a novel refined analysis of this greedy heuristic which enables us to: (1)(1) reduce the enumeration in the tight (1e1)(1-e^{-1})-approximation of [Sviridenko 04] from subsets of size three to two; (2)(2) present an improved upper bound of 0.429450.42945 for the classic algorithm which returns the better between a single element and the output of the greedy heuristic.

Keywords

Cite

@article{arxiv.2102.12879,
  title  = {A Refined Analysis of Submodular Greedy},
  author = {Ariel Kulik and Roy Schwartz and Hadas Shachnai},
  journal= {arXiv preprint arXiv:2102.12879},
  year   = {2021}
}
R2 v1 2026-06-23T23:30:30.077Z