A faster algorithm for solving general LPs

Shunhua Jiang, Zhao Song, Omri Weinstein, Hengjie Zhang

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

30 Scopus citations

Abstract

The fastest known LP solver for general (dense) linear programs is due to [Cohen, Lee and Song'19] and runs in O?(n? +n2.5-?/2 + n2+1/6) time. A number of follow-up works [Lee, Song and Zhang'19, Brand'20, Song and Yu'20] obtain the same complexity through different techniques, but none of them can go below n2+1/6, even if ?=2. This leaves a polynomial gap between the cost of solving linear systems (n?) and the cost of solving linear programs, and as such, improving the n2+1/6 term is crucial toward establishing an equivalence between these two fundamental problems. In this paper, we reduce the running time to O?(n? +n2.5-?/2 + n2+1/18) where ? and ? are the fast matrix multiplication exponent and its dual. Hence, under the common belief that ? ? 2 and ? ? 1, our LP solver runs in O?(n2.055) time instead of O?(n2.16).

Original languageAmerican English
Title of host publicationSTOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
EditorsSamir Khuller, Virginia Vassilevska Williams
PublisherAssociation for Computing Machinery
Pages823-832
Number of pages10
ISBN (Electronic)9781450380539
DOIs
StatePublished - 15 Jun 2021
Externally publishedYes
Event53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy
Duration: 21 Jun 202125 Jun 2021

Publication series

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

Conference

Conference53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Country/TerritoryItaly
CityVirtual, Online
Period21/06/2125/06/21

Bibliographical note

Publisher Copyright:
© 2021 ACM.

Keywords

  • Convex optimization
  • Dynamic data-structure
  • Linear programming

Fingerprint

Dive into the research topics of 'A faster algorithm for solving general LPs'. Together they form a unique fingerprint.

Cite this