Explicit expanding expanders

Michael Dinitz, Michael Schapira, Asaf Valadarsky

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

1 Scopus citations

Abstract

Deterministic constructions of expander graphs have been an important topic of research in computer science and mathematics, with many well-studied constructions of infinite families of expanders. In some applications, though, an infinite family is not enough: we need expanders which are “close” to each other. We study the following question: Construct an an infinite sequence of expanders G0,G1, . . . , such that for every two consecutive graphs Gi and Gi+1, Gi+1 can be obtained from Gi by adding a single vertex and inserting/removing a small number of edges, which we call the expansion cost of transitioning from Gi to Gi+1. This question is very natural, e.g., in the context of datacenter networks, where the vertices represent racks of servers, and the expansion cost captures the amount of rewiring needed when adding another rack to the network. We present an explicit construction of d-regular expanders with expansion cost at most [formula presented] , for any d ≥ 6. Our construction leverages the notion of a “2-lift” of a graph. This operation was first analyzed by Bilu and Linial [1], who repeatedly applied 2-lifts to construct an infinite family of expanders which double in size from one expander to the next. Our construction can be viewed as a way to “interpolate” between Bilu-Linial expanders with low expansion cost while preserving good edge expansion throughout.

Original languageAmerican English
Title of host publicationAlgorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
EditorsNikhil Bansal, Irene Finocchi
PublisherSpringer Verlag
Pages399-410
Number of pages12
ISBN (Print)9783662483497
DOIs
StatePublished - 2015
Event23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece
Duration: 14 Sep 201516 Sep 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9294
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd European Symposium on Algorithms, ESA 2015
Country/TerritoryGreece
CityPatras
Period14/09/1516/09/15

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

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