New streaming algorithms for high dimensional EMD and MST

Xi Chen, Rajesh Jayaram, Amit Levi, Erik Waingarten

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We study streaming algorithms for two fundamental geometric problems: computing the cost of a Minimum Spanning Tree (MST) of an n-point set X g {1,2 "}d, and computing the Earth Mover Distance (EMD) between two multi-sets A,B g {1,2 "}d of size n. We consider the turnstile model, where points can be added and removed. We give a one-pass streaming algorithm for MST and a two-pass streaming algorithm for EMD, both achieving an approximation factor of Õ(logn) and using (n,d,")-space only. Furthermore, our algorithm for EMD can be compressed to a single pass with a small additive error. Previously, the best known sublinear-space streaming algorithms for either problem achieved an approximation of O(min{ logn , log(Δd)} logn). For MST, we also prove that any constant space streaming algorithm can only achieve an approximation of ω(logn), analogous to the ω(logn) lower bound for EMD. Our algorithms are based on an improved analysis of a recursive space partitioning method known generically as the Quadtree. Specifically, we show that the Quadtree achieves an Õ(logn) approximation for both EMD and MST, improving on the O(min{ logn , log(Δd)} logn) approximation.

Original languageEnglish
Title of host publicationSTOC 2022 - Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing
EditorsStefano Leonardi, Anupam Gupta
PublisherAssociation for Computing Machinery
Number of pages12
ISBN (Electronic)9781450392648
StatePublished - 6 Sep 2022
Externally publishedYes
Event54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022 - Rome, Italy
Duration: 20 Jun 202224 Jun 2022

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017


Conference54th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2022

Bibliographical note

Publisher Copyright:
© 2022 Owner/Author.


  • earth-mover's distance
  • minimum spanning tree
  • sketching
  • streaming

ASJC Scopus subject areas

  • Software


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