@inproceedings{56f7f9f37cae4a71afcb3b267952afbe,
title = "Towards resistance sparsifiers",
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 {\~O}(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.",
keywords = "Commute time, Edge sparsification, Effective resistance, Graph expansion, Spectral sparsifier",
author = "Michael Dinitz and Robert Krauthgamer and Tal Wagner",
note = "Publisher Copyright: {\textcopyright} Michael Dinitz, Robert Krauthgamer, and Tal Wagner.; 18th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2015, and 19th International Workshop on Randomization and Computation, RANDOM 2015 ; Conference date: 24-08-2015 Through 26-08-2015",
year = "2015",
month = aug,
day = "1",
doi = "10.4230/LIPIcs.APPROX-RANDOM.2015.738",
language = "אנגלית",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "738--755",
editor = "Naveen Garg and Klaus Jansen and Anup Rao and Rolim, {Jose D. P.}",
booktitle = "Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 18th International Workshop, APPROX 2015, and 19th International Workshop, RANDOM 2015",
}