A clutter L is a collection of m subsets of a ground set E(L)={x1,...,xn} with the property that for every pair Ai, Aj∈L, Ai is neither contained nor contains Aj. A transversal of L is a subset of E(L) having at least one element in common with each member of L. The problem of finding the minimum weight transversal of a clutter L is equivalent to the well-known set covering problem. In this paper the class of ideal clutters that properly contains the class of clutters the members of which are the bases of a matroid (matroidal clutters) is introduced. An ideal clutter L has the property that the number of its minimal transversals is bounded by a polynomial in m and n. The properties of ideal clutters are described, and two polynomial algorithms for recognizing them and finding their minimum weight transversal are presented.
