On Bounds for Greedy Schemes in String Optimization based on Greedy Curvatures
Abstract
We consider the celebrated bound introduced by Conforti and Cornu\'ejols (1984) for greedy schemes in submodular optimization. The bound assumes a submodular function defined on a collection of sets forming a matroid and is based on greedy curvature. We show that the bound holds for a very general class of string problems that includes maximizing submodular functions over set matroids as a special case. We also derive a bound that is computable in the sense that they depend only on quantities along the greedy trajectory. We prove that our bound is superior to the greedy curvature bound of Conforti and Cornu\'ejols. In addition, our bound holds under a condition that is weaker than submodularity.
Cite
@article{arxiv.2404.06669,
title = {On Bounds for Greedy Schemes in String Optimization based on Greedy Curvatures},
author = {Bowen Li and Brandon Van Over and Edwin K. P. Chong and Ali Pezeshki},
journal= {arXiv preprint arXiv:2404.06669},
year = {2024}
}
Comments
This version has been accepted as an invited paper in the 63rd IEEE Conference on Decision and Control, Milan, Italy, December 16--19, 2024