Well-Scaling Procedure for Deciding Gammoid Class-Membership of Matroids

TL;DR

This paper presents a scalable procedure for determining whether a given matroid is a gammoid, using a tableau-based approach that efficiently guides the decision process and is suitable for parallel computation.

Contribution

It introduces a novel tableau-based method with rules and steps that efficiently decide gammoid membership in matroids, improving scalability.

Findings

The procedure effectively determines gammoid class-membership.

The method scales well with parallel computation models.

It provides a systematic framework for matroid property decision problems.

Abstract

We introduce a procedure that solves the decision problem whether a given matroid M is a gammoid. The procedure consists of three pieces: First, we introduce a notion of a valid matroid tableau which captures the current state of knowledge regarding the properties of matroids related to the matroid under consideration. Second, we give a sufficient set of rules that may be used to generate valid matroid tableaux. Third, we introduce a succession of steps that ultimately lead to a decisive tableau starting with any valid tableau. We argue that the decision problem scales well with respect to parallel computation models.