Computer Science > Data Structures and Algorithms
arXiv:2606.24845 (cs)
[Submitted on 23 Jun 2026]
Abstract:We settle the classic question of the parallel complexity of computing a matroid basis, as first posed in the seminal work of Karp, Upfal, and Wigderson (FOCS 1985, JCSS 1988). Our algorithm runs in $O(n^{1/3}\log^{1/3}n)$ rounds, matching the lower bound of KUW up to a $\log^{2/3}(n)$ factor.
Submission history
From: Aaron (Louie) Putterman [view email]
[v1]
Tue, 23 Jun 2026 17:24:37 UTC (56 KB)
Bibliographic Tools
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Code, Data, Media
Code, Data and Media Associated with this Article
Demos
Demos
Related Papers
Recommenders and Search Tools
About arXivLabs
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

























