Spectral sparsification via bounded-independence sampling

Dean Doron, Jack Murtagh, Salil Vadhan, David Zuckerman

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

2 Scopus citations

Abstract

We give a deterministic, nearly logarithmic-space algorithm for mild spectral sparsification of undirected graphs. Given a weighted, undirected graph G on n vertices described by a binary string of length N, an integer k ≤ log n and an error parameter ε > 0, our algorithm runs in space Oe(klog(N · wmax/wmin)) where wmax and wmin are the maximum and minimum edge weights in G, and produces a weighted graph H with Oe(n1+2/k2) edges that spectrally approximates G, in the sense of Spielmen and Teng [52], up to an error of ε. Our algorithm is based on a new bounded-independence analysis of Spielman and Srivastava's effective resistance based edge sampling algorithm [51] and uses results from recent work on space-bounded Laplacian solvers [41]. In particular, we demonstrate an inherent tradeoff (via upper and lower bounds) between the amount of (bounded) independence used in the edge sampling algorithm, denoted by k above, and the resulting sparsity that can be achieved.

Original languageEnglish
Title of host publication47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
EditorsArtur Czumaj, Anuj Dawar, Emanuela Merelli
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771382
DOIs
StatePublished - 1 Jun 2020
Externally publishedYes
Event47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 - Virtual, Online, Germany
Duration: 8 Jul 202011 Jul 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume168
ISSN (Print)1868-8969

Conference

Conference47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
Country/TerritoryGermany
CityVirtual, Online
Period8/07/2011/07/20

Keywords

  • Derandomization
  • Space complexity
  • Spectral sparsification

ASJC Scopus subject areas

  • Software

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