An improved algorithm for recognizing matroids

Brahim Chaourar

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arXiv · 1709.10258

An improved algorithm for recognizing matroids

Brahim Chaourar

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Abstract

Let $M$ be a matroid defined on a finite set $E$ and $L\subset E$. $L$ is locked in $M$ if $M|L$ and $M^*|(E\backslash L)$ are 2-connected, and $min\{r(L), r^*(E\backslash L)\} \geq 2$. Locked subsets characterize nontrivial facets of the bases polytope. In this paper, we give a new axiom system for matroids based on locked subsets. We deduce an algorithm for recognizing matroids improving the running time complexity of the best known till today. This algorithm induces a polynomial time algorithm for recognizing uniform matroids. This latter problem is intractable if we use an independence oracle.

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BibTeX RIS

Brahim Chaourar. 2019-06-18. An improved algorithm for recognizing matroids. https://arxiv.org/abs/1709.10258

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