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Matroid complexity and nonsuccinct descriptions
 SIAM J. Discret. Math
"... Abstract. We investigate an approach to matroid complexity that involves describing a matroid via a list of independent sets, bases, circuits, or some other family of subsets of the ground set. The computational complexity of algorithmic problems under this scheme appears to be highly dependent on ..."
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Abstract. We investigate an approach to matroid complexity that involves describing a matroid via a list of independent sets, bases, circuits, or some other family of subsets of the ground set. The computational complexity of algorithmic problems under this scheme appears to be highly dependent on the choice of input type. We define an order on the various methods of description, and we show how this order acts upon 10 types of input. We also show that under this approach several natural algorithmic problems are complete in classes thought not to be equal to P.