Recognizing Matroids

09/29/2017

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by   Brahim Chaourar, et al.

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Let E be a finite set and P, S, L three classes of subsets of E, and r a function defined on 2^E. In this paper, we give an algorithm for testing if the quadruple ( P, S, L, r) is the locked structure of a given matroid, i.e., recognizing if ( P, S, L, r) defines a matroid. This problem is intractable. Our algorithm improves the running time complexity of a previous algorithm due to Spinrad. We deduce a polynomial time algorithm for recognizing large classes of matroids called polynomially locked matroids and uniform matroids.