The matroid intersection cover problem

We consider the matroid intersection cover problem. This is a special case of set cover where the sets are derived from the intersection of matroids. We introduce a technique for computing matroid intersection covers. We give polynomial-time algorithms to compute partition decompositions for matroids that commonly arise in combinatorial optimization problems. We then give a polynomial-time algorithm for computing matroid intersection covers given the partition decompositions of the matroids. Combining these algorithms, we obtain an O ( 1 ) -approximation algorithm when each of the O ( 1 ) matroids is of a standard type.