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Bravely, Moderately: A Common Theme in Four Recent Works

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Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6650))

Abstract

We highlight a common theme in four relatively recent works that establish remarkable results by an iterative approach. Starting from a trivial construct, each of these works applies an ingeniously designed sequence of iterations that yields the desired result, which is highly non-trivial. Furthermore, in each iteration, the construct is modified in a relatively moderate manner. The four works we refer to are

  1. 1

    the polynomial-time approximation of the permanent of non-negative matrices (by Jerrum, Sinclair, and Vigoda, 33rd STOC, 2001);

  2. 2

    the iterative (Zig-Zag) construction of expander graphs (by Reingold, Vadhan, and Wigderson, 41st FOCS, 2000);

  3. 3

    the log-space algorithm for undirected connectivity (by Reingold, 37th STOC, 2005);

  4. 4

    and, the alternative proof of the PCP Theorem (by Dinur, 38th STOC, 2006).

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Authors
  1. Oded Goldreich
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Editors and Affiliations

  1. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, 76100, Rehovot, Israel

    Oded Goldreich

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Goldreich, O. (2011). Bravely, Moderately: A Common Theme in Four Recent Works. In: Goldreich, O. (eds) Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation. Lecture Notes in Computer Science, vol 6650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22670-0_26

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  • DOI: https://doi.org/10.1007/978-3-642-22670-0_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22669-4

  • Online ISBN: 978-3-642-22670-0

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