Multi-parametric matroids -- Applications to interdiction and weight set decomposition
Abstract
In this article, we investigate the multi-parametric matroid problem. The weights of the elements of the matroid's ground set depend linearly on an arbitrary but fixed number of parameters, each of which is taken from a real interval. The goal is to compute a minimum weight basis for each possible combination of the parameters. For this problem, we propose an algorithm that requires a polynomial number of independence tests and discuss two useful applications. First, the algorithm can be applied to solve a multi-parametric version of a special matroid interdiction problem, and second, it can be utilized to compute the weight set decomposition of the multi-objective (graphic) matroid problem. For the latter, we asymptotically improve the current state-of-the-art algorithm by a factor that is almost proportional to the number of edges of the graphic matroid.
Cite
@article{arxiv.2503.08178,
title = {Multi-parametric matroids -- Applications to interdiction and weight set decomposition},
author = {Nils Hausbrandt and Stefan Ruzika},
journal= {arXiv preprint arXiv:2503.08178},
year = {2025}
}