Shifted Matroid Optimization

TL;DR

This paper demonstrates that the problem of finding lexicographically minimal bases in a matroid can be solved efficiently in polynomial time, extending to a more general shifted problem over matroids.

Contribution

It introduces a polynomial-time algorithm for the shifted matroid optimization problem, generalizing the approach to a broader class of problems.

Findings

Polynomial-time algorithm for lexicographically minimal bases

Extension to shifted matroid optimization problem

Efficient solutions in the oracle model

Abstract

We show that finding lexicographically minimal $n$ bases in a matroid can be done in polynomial time in the oracle model. This follows from a more general result that the shifted problem over a matroid can be solved in polynomial time as well.