Fast greedy for linear matroids

Abstract

A fundamental algorithmic result for matroids is that the maximum weight base can be computed using the greedy algorithm. For explicitly represented matroids an important question is the time complexity of computing such a base. It is known that one can compute it in time almost linear in the number of non-zero entries of the linear representation plus rω, where r is the rank of the matroid and ω is the matrix multiplication exponent. In this work, we give an alternative algorithm for the same task.