Towards resistance sparsifiers

Michael Dinitz, Robert Krauthgamer, Tal Wagner

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

11 Scopus citations

Abstract

We study resistance sparsification of graphs, in which the goal is to find a sparse subgraph (with reweighted edges) that approximately preserves the effective resistances between every pair of nodes. We show that every dense regular expander admits a (1 + ∈)-resistance sparsifier of size Õ(n/∈), and conjecture this bound holds for all graphs on n nodes. In comparison, spectral sparsification is a strictly stronger notion and requires Ω (n/∈2) edges even on the complete graph. Our approach leads to the following structural question on graphs: Does every dense regular expander contain a sparse regular expander as a subgraph? Our main technical contribution, which may of independent interest, is a positive answer to this question in a certain setting of parameters. Combining this with a recent result of von Luxburg, Radl, and Hein [16] leads to the aforementioned resistance sparsifiers.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 18th International Workshop, APPROX 2015, and 19th International Workshop, RANDOM 2015
EditorsNaveen Garg, Klaus Jansen, Anup Rao, Jose D. P. Rolim
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages738-755
Number of pages18
ISBN (Electronic)9783939897897
DOIs
StatePublished - 1 Aug 2015
Externally publishedYes
Event18th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2015, and 19th International Workshop on Randomization and Computation, RANDOM 2015 - Princeton, United States
Duration: 24 Aug 201526 Aug 2015

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume40
ISSN (Print)1868-8969

Conference

Conference18th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2015, and 19th International Workshop on Randomization and Computation, RANDOM 2015
Country/TerritoryUnited States
CityPrinceton
Period24/08/1526/08/15

Keywords

  • Commute time
  • Edge sparsification
  • Effective resistance
  • Graph expansion
  • Spectral sparsifier

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