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Erdős-Rényi Sequences and Deterministic Construction of Expanding Cayley Graphs

  • Vikraman Arvind
  • Partha Mukhopadhyay
  • Prajakta Nimbhorkar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7256)

Abstract

Given a finite group G by its multiplication table, we give a deterministic polynomial-time construction of a directed O(log|G|) degree Cayley expander for G. Our construction exploits the connection between rapid mixing random walks and spectral expansion. Our main group-theoretic tool is Erdős-Rényi sequences. We give a similar construction of O(log|G|) degree undirected Cayley expanders for G, which is an alternative proof of Wigderson and Xiao’s derandomization [WX08] of the Alon-Roichman randomized construction.

Keywords

Cayley Graph Random Element Expander Graph Distinct Index Ramanujan Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vikraman Arvind
    • 1
  • Partha Mukhopadhyay
    • 2
  • Prajakta Nimbhorkar
    • 2
  1. 1.The Institute of Mathematical SciencesChennaiIndia
  2. 2.Chennai Mathematical InstituteSiruseriIndia

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