Matroid reinforcement and sparsification
Combinatorics
2024-08-02 v1
Abstract
Homogeneous matroids are characterized by the property that strength equals fractional arboricity, and arise in the study of base modulus [22]. For graphic matroids, Cunningham [9] provided efficient algorithms for calculating graph strength, and also for determining minimum cost reinforcement to achieve a desired strength. This paper extends this latter problem by focusing on two optimal strategies for transforming a matroid into a homogeneous one, by either increasing or decreasing element weights. As an application to graphs, we give algorithms to solve this problem in the context of spanning trees.
Cite
@article{arxiv.2408.00173,
title = {Matroid reinforcement and sparsification},
author = {Huy Truong and Pietro Poggi-Corradini},
journal= {arXiv preprint arXiv:2408.00173},
year = {2024}
}