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Erdős-Rényi Sequences and Deterministic Construction of Expanding Cayley Graphs

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Part of the Lecture Notes in Computer Science book series (LNTCS,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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References

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Arvind, V., Mukhopadhyay, P., Nimbhorkar, P. (2012). Erdős-Rényi Sequences and Deterministic Construction of Expanding Cayley Graphs. In: Fernández-Baca, D. (eds) LATIN 2012: Theoretical Informatics. LATIN 2012. Lecture Notes in Computer Science, vol 7256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29344-3_4

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  • DOI: https://doi.org/10.1007/978-3-642-29344-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29343-6

  • Online ISBN: 978-3-642-29344-3

  • eBook Packages: Computer ScienceComputer Science (R0)