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Bibliographic Details
Main Authors: Hausbrandt, Nils, Ruzika, Stefan
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.08178
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Table of Contents:
  • 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.