Breaking O(nr) for Matroid Intersection

05/12/2021 ∙ by Joakim Blikstad, et al. ∙ 0

We present algorithms that break the Õ(nr)-independence-query bound for the Matroid Intersection problem for the full range of r; where n is the size of the ground set and r≤ n is the size of the largest common independent set. The Õ(nr) bound was due to the efficient implementations [CLSSW FOCS'19; Nguyen 2019] of the classic algorithm of Cunningham [SICOMP'86]. It was recently broken for large r (r=ω(√(n))), first by the Õ(n^1.5/ϵ^1.5)-query (1-ϵ)-approximation algorithm of CLSSW [FOCS'19], and subsequently by the Õ(n^6/5r^3/5)-query exact algorithm of BvdBMN [STOC'21]. No algorithm, even an approximation one, was known to break the Õ(nr) bound for the full range of r. We present an Õ(n√(r)/ϵ)-query (1-ϵ)-approximation algorithm and an Õ(nr^3/4)-query exact algorithm. Our algorithms improve the Õ(nr) bound and also the bounds by CLSSW and BvdBMN for the full range of r.



There are no comments yet.


page 1

page 2

page 3

page 4

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.