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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

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.