License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
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DOI: 10.4230/LIPIcs.ISAAC.2021.73
URN: urn:nbn:de:0030-drops-155061
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15506/
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Biabani, Leyla ; de Berg, Mark ; Monemizadeh, Morteza

Maximum-Weight Matching in Sliding Windows and Beyond

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Abstract

We study the maximum-weight matching problem in the sliding-window model. In this model, we are given an adversarially ordered stream of edges of an underlying edge-weighted graph G(V,E), and a parameter L specifying the window size, and we want to maintain an approximation of the maximum-weight matching of the current graph G(t); here G(t) is defined as the subgraph of G consisting of the edges that arrived during the time interval [max(t-L,1),t], where t is the current time. The goal is to do this with Õ(n) space, where n is the number of vertices of G. We present a deterministic (3.5+ε)-approximation algorithm for this problem, thus significantly improving the (6+ε)-approximation algorithm due to Crouch and Stubbs [Michael S. Crouch and Daniel M. Stubbs, 2014].
We also present a generic machinery for approximating subadditve functions in the sliding-window model. A function f is called subadditive if for every disjoint substreams A, B of a stream S it holds that f(AB) ⩽ f(A) + f(B), where AB denotes the concatenation of A and B. We show that given an α-approximation algorithm for a subadditive function f in the insertion-only model we can maintain a (2α+ε)-approximation of f in the sliding-window model. This improves upon recent result Krauthgamer and Reitblat [Robert Krauthgamer and David Reitblat, 2019], who obtained a (2α²+ε)-approximation.

BibTeX - Entry

@InProceedings{biabani_et_al:LIPIcs.ISAAC.2021.73,
  author =	{Biabani, Leyla and de Berg, Mark and Monemizadeh, Morteza},
  title =	{{Maximum-Weight Matching in Sliding Windows and Beyond}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{73:1--73:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15506},
  URN =		{urn:nbn:de:0030-drops-155061},
  doi =		{10.4230/LIPIcs.ISAAC.2021.73},
  annote =	{Keywords: maximum-weight matching, sliding-window model, approximation algorithm, and subadditve functions}
}

Keywords: maximum-weight matching, sliding-window model, approximation algorithm, and subadditve functions
Collection: 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Issue Date: 2021
Date of publication: 30.11.2021

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