Optimizing Polymatroid Functions
Data Structures and Algorithms
2022-11-16 v1
Abstract
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming technique, based on duality and projections, can be used to rederive some structural results that were previously established using more ad hoc methods. We then show that this technique can be used to obtain a polynomial-time algorithm for a certain type of simple difference constraints. Finally we give lower bound results that show that certain possible extensions of these results are probably not feasible.
Cite
@article{arxiv.2211.08381,
title = {Optimizing Polymatroid Functions},
author = {Sungjin Im and Benjamin Moseley and Hung Q. Ngo and Kirk Pruhs and Alireza Samadian},
journal= {arXiv preprint arXiv:2211.08381},
year = {2022}
}