License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2023.88
URN: urn:nbn:de:0030-drops-181408
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18140/
Go to the corresponding LIPIcs Volume Portal

Liu, S. Cliff ; Song, Zhao ; Zhang, Hengjie ; Zhang, Lichen ; Zhou, Tianyi

Space-Efficient Interior Point Method, with Applications to Linear Programming and Maximum Weight Bipartite Matching

pdf-format:
LIPIcs-ICALP-2023-88.pdf (0.8 MB)

Abstract

We study the problem of solving linear program in the streaming model. Given a constraint matrix A ∈ ℝ^{m×n} and vectors b ∈ ℝ^m, c ∈ ℝ^n, we develop a space-efficient interior point method that optimizes solely on the dual program. To this end, we obtain efficient algorithms for various different problems:
- For general linear programs, we can solve them in Õ(√n log(1/ε)) passes and Õ(n²) space for an ε-approximate solution. To the best of our knowledge, this is the most efficient LP solver in streaming with no polynomial dependence on m for both space and passes.
- For bipartite graphs, we can solve the minimum vertex cover and maximum weight matching problem in Õ(√m) passes and Õ(n) space.
In addition to our space-efficient IPM, we also give algorithms for solving SDD systems and isolation lemma in Õ(n) spaces, which are the cornerstones for our graph results.

BibTeX - Entry

@InProceedings{liu_et_al:LIPIcs.ICALP.2023.88,
  author =	{Liu, S. Cliff and Song, Zhao and Zhang, Hengjie and Zhang, Lichen and Zhou, Tianyi},
  title =	{{Space-Efficient Interior Point Method, with Applications to Linear Programming and Maximum Weight Bipartite Matching}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{88:1--88:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18140},
  URN =		{urn:nbn:de:0030-drops-181408},
  doi =		{10.4230/LIPIcs.ICALP.2023.88},
  annote =	{Keywords: Convex optimization, interior point method, streaming algorithm}
}

Keywords: Convex optimization, interior point method, streaming algorithm
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI