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 polynomialtime 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. (c) 2020 Elsevier B.V. All rights reserved.