Consider selling bundles of indivisible goods to buyers with concave utilities that are additively separable in money and goods. We propose an ascending auction for the case when the seller is constrained to sell bundles whose elements form a basis of a matroid. It extends easily to polymatroids. Applications include scheduling, allocation of homogeneous goods, and spatially distributed markets, among others. Our ascending auction induces buyers to bid truthfully and returns the economically

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... icient basis. Unlike other ascending auctions for this environment, ours runs in pseudopolynomial or polynomial time. Furthermore, we prove the impossibility of an ascending auction for nonmatroidal independence setsystems.