License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2020.33
URN: urn:nbn:de:0030-drops-132746
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13274/
Go to the corresponding LIPIcs Volume Portal

Wasim, Omer ; King, Valerie

Fully Dynamic Sequential and Distributed Algorithms for MAX-CUT

pdf-format:
LIPIcs-FSTTCS-2020-33.pdf (0.5 MB)

Abstract

This paper initiates the study of the MAX-CUT problem in fully dynamic graphs. Given a graph G = (V,E), we present deterministic fully dynamic distributed and sequential algorithms to maintain a cut on G which always contains at least |E|/2 edges in sublinear update time under edge insertions and deletions to G. Our results include the following deterministic algorithms: i) an O(Δ) worst-case update time sequential algorithm, where Δ denotes the maximum degree of G, ii) the first fully dynamic distributed algorithm taking O(1) rounds and O(Δ) total bits of communication per update in the Massively Parallel Computation (MPC) model with n machines and O(n) words of memory per machine. The aforementioned algorithms require at most one adjustment, that is, a move of one vertex from one side of the cut to the other.
We also give the following fully dynamic sequential algorithms: i) a deterministic O(m^{1/2}) amortized update time algorithm where m denotes the maximum number of edges in G during any sequence of updates and, ii) a randomized algorithm which takes Õ(n^{2/3}) worst-case update time when edge updates come from an oblivious adversary.

BibTeX - Entry

@InProceedings{wasim_et_al:LIPIcs:2020:13274,
  author =	{Omer Wasim and Valerie King},
  title =	{{Fully Dynamic Sequential and Distributed Algorithms for MAX-CUT}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{33:1--33:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Nitin Saxena and Sunil Simon},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13274},
  URN =		{urn:nbn:de:0030-drops-132746},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.33},
  annote =	{Keywords: data structures, dynamic graph algorithms, approximate maximum cut, distributed computing, parallel computing}
}

Keywords: data structures, dynamic graph algorithms, approximate maximum cut, distributed computing, parallel computing
Collection: 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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