On some algorithmic aspects of hypergraphic matroids

TL;DR

This paper extends several algorithms from graphic matroids to hypergraphic matroids, addressing problems like independence testing, rank computation, and network reinforcement, thus advancing the understanding of hypergraphic matroid algorithms.

Contribution

It demonstrates that multiple algorithms for graphic matroids can be adapted to hypergraphic matroids, broadening their applicability.

Findings

Algorithms for the separation problem are extendable to hypergraphic matroids.

Methods for testing independence are applicable to hypergraphic matroids.

Computations of rank, strength, and arboricity are feasible for hypergraphic matroids.

Abstract

Hypergraphics matroids were studied first by Lorea and later by Frank et al. They can be seen as generalizations of graphic matroids. Here we show that several algorithms developed for the graphic case can be extended to hypergraphic matroids. We treat the following: the separation problem for the associated polytope, testing independence, separation of partition inequalities, computing the rank of a set, computing the strength, computing the arboricity and network reinforcement.