English

A Weighted-to-Unweighted Reduction for Matroid Intersection

Data Structures and Algorithms 2026-02-18 v1

Abstract

Given two matroids M1\mathcal{M}_1 and M2\mathcal{M}_2 over the same ground set, the matroid intersection problem is to find the maximum cardinality common independent set. In the weighted version of the problem, the goal is to find a maximum weight common independent set. It has been a matter of interest to find efficient approximation algorithms for this problem in various settings. In many of these models, there is a gap between the best known results for the unweighted and weighted versions. In this work, we address the question of closing this gap. Our main result is a reduction which converts any α\alpha-approximate unweighted matroid intersection algorithm into an α(1ε)\alpha(1-\varepsilon)-approximate weighted matroid intersection algorithm, while increasing the runtime of the algorithm by a logW\log W factor, where WW is the aspect ratio. Our framework is versatile and translates to settings such as streaming and one-way communication complexity where matroid intersection is well-studied. As a by-product of our techniques, we derive new results for weighted matroid intersection in these models.

Keywords

Cite

@article{arxiv.2602.15702,
  title  = {A Weighted-to-Unweighted Reduction for Matroid Intersection},
  author = {Aditi Dudeja and Mara Grilnberger},
  journal= {arXiv preprint arXiv:2602.15702},
  year   = {2026}
}

Comments

37 pages, accepted to IPCO

R2 v1 2026-07-01T10:40:08.166Z