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.ITCS.2023.50
URN: urn:nbn:de:0030-drops-175534
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17553/
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Filtser, Arnold ; Kapralov, Michael ; Makarov, Mikhail

Expander Decomposition in Dynamic Streams

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LIPIcs-ITCS-2023-50.pdf (0.6 MB)

Abstract

In this paper we initiate the study of expander decompositions of a graph G = (V, E) in the streaming model of computation. The goal is to find a partitioning ? of vertices V such that the subgraphs of G induced by the clusters C ∈ ? are good expanders, while the number of intercluster edges is small. Expander decompositions are classically constructed by a recursively applying balanced sparse cuts to the input graph. In this paper we give the first implementation of such a recursive sparsest cut process using small space in the dynamic streaming model.
Our main algorithmic tool is a new type of cut sparsifier that we refer to as a power cut sparsifier - it preserves cuts in any given vertex induced subgraph (or, any cluster in a fixed partition of V) to within a (δ, ε)-multiplicative/additive error with high probability. The power cut sparsifier uses Õ(n/εδ) space and edges, which we show is asymptotically tight up to polylogarithmic factors in n for constant δ.

BibTeX - Entry

@InProceedings{filtser_et_al:LIPIcs.ITCS.2023.50,
  author =	{Filtser, Arnold and Kapralov, Michael and Makarov, Mikhail},
  title =	{{Expander Decomposition in Dynamic Streams}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{50:1--50:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17553},
  URN =		{urn:nbn:de:0030-drops-175534},
  doi =		{10.4230/LIPIcs.ITCS.2023.50},
  annote =	{Keywords: Streaming, expander decomposition, graph sparsifiers}
}

Keywords: Streaming, expander decomposition, graph sparsifiers
Collection: 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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