We initiate the study of matroid problems in a new oracle model called dynamic oracle. Our
algorithms in this model lead to new bounds for some classic problems, and a “unified” …

We consider the matroid intersection problem in the independence oracle model. Given two
matroids over n common elements such that the intersection has rank k, our main technique …

Matroids are a fundamental object of study in combinatorial optimization. Three closely
related and important problems involving matroids are maximizing the size of the union of k …

We present algorithms that break the $\tilde O (nr) $-independence-query bound for the
Matroid Intersection problem for the full range of $ r $; where $ n $ is the size of the ground …

Submodular function minimization (SFM) and matroid intersection are fundamental discrete
optimization problems with applications in many fields. It is well known that both of these can …

Given two matroids M 1 and M 2 over the same n-element ground set, the matroid
intersection problem is to find a largest common independent set, whose size we denote by …

We consider fast algorithms for monotone submodular maximization with a general matroid
constraint. We present a randomized $(1-1/e-\epsilon) $-approximation algorithm that …

In the matroid partitioning problem, we are given $ k $ matroids $\mathcal {M}
_1=(V,\mathcal {I} _1),\dots,\mathcal {M} _k=(V,\mathcal {I} _k) $ defined over a common …

Given two matroids $\mathcal {M} _1=(V,\mathcal {I} _1) $ and $\mathcal {M} _2=(V,\mathcal
{I} _2) $ over an $ n $-element integer-weighted ground set $ V $, the weighted matroid …

In the matroid intersection problem, we are given two matroids $\mathcal {M} _1=(V,\mathcal
{I} _1) $ and $\mathcal {M} _2=(V,\mathcal {I} _2) $ defined on the same ground set $ V $ of …