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Zigzag Products, Expander Constructions, Connections, and Applications

  • Conference paper
FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2914))

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Abstract

Expansion of graphs can be given equivalent definitions in combinatorial and algebraic terms. This is the most basic connection between combinatorics and algebra illuminated by expanders and the quest to construct them. The talk will survey how fertile this connection has been to both fields, focusing on recent results. In particular, I will explain the zigzag product, and how it enables better constructions and new applications.

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References

  1. Reingold, O., Vadhan, S., Wigderson, A.: Entropy Waves, the Zig-zag Graph Product, and New Constant Degree Expanders. Annals of Mathematics 155(1), 157–187 (2002)

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  2. Alon, N., Lubotzky, A., Wigderson, A.: Semi-direct product in groups and Zigzag product in graphs: Connections and applications. In: Proc. of the 42nd FOCS, pp. 630–637 (2001)

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  3. Capalbo, M., Reingold, O., Vadhan, S., Wigderson, A.: Randomness Conductors and Constant-Degree Expansion Beyond the Degree/2 Barrier. In: Proc. of the 34th STOC, pp. 659–668 (2002)

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  4. Meshulam, R., Wigderson, A.: Expanders in Group Algebras. Combinatorica (2003) (to appear), available at http://www.math.ias.edu/~avi/PUBLICATIONS/

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Author information

Authors and Affiliations

  1. The Institute of Advanced Studies, Princeton, USA

    Avi Wigderson

  2. The Hebrew University, Jerusalem, Israel

    Avi Wigderson

Authors
  1. Avi Wigderson
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Editor information

Editors and Affiliations

  1. Tata Institute of Fundamental Research, India

    Paritosh K. Pandya

  2. Tata Institute of Fundamental Research, School of Technology and Computer Science, Mumbai, India

    Jaikumar Radhakrishnan

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© 2003 Springer-Verlag Berlin Heidelberg

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Wigderson, A. (2003). Zigzag Products, Expander Constructions, Connections, and Applications. In: Pandya, P.K., Radhakrishnan, J. (eds) FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2003. Lecture Notes in Computer Science, vol 2914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24597-1_38

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  • DOI: https://doi.org/10.1007/978-3-540-24597-1_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20680-4

  • Online ISBN: 978-3-540-24597-1

  • eBook Packages: Springer Book Archive

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