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Information Complexity versus Corruption and Applications to Orthogonality and Gap-Hamming

  • Amit Chakrabarti
  • Ranganath Kondapally
  • Zhenghui Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7408)

Abstract

Three decades of research in communication complexity have led to the invention of a number of techniques to lower bound randomized communication complexity. The majority of these techniques involve properties of large submatrices (rectangles) of the truth-table matrix defining a communication problem. The only technique that does not quite fit is information complexity, which has been investigated over the last decade. Here, we connect information complexity to one of the most powerful “rectangular” techniques: the recently-introduced smooth corruption (or “smooth rectangle”) bound. We show that the former subsumes the latter under rectangular input distributions.

As an application, we obtain an optimal Ω(n) lower bound on the information complexity—under the uniform distribution—of the so-called orthogonality problem (ORT), which is in turn closely related to the much-studied Gap-Hamming-Distance problem (GHD). The proof of this bound is along the lines of recent communication lower bounds for GHD, but we encounter a surprising amount of additional technical detail.

Keywords

Communication Complexity Information Complexity Corruption Gap Hamming Orthogonality 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Amit Chakrabarti
    • 1
  • Ranganath Kondapally
    • 1
  • Zhenghui Wang
    • 1
  1. 1.Department of Computer ScienceDartmouth CollegeHanoverUSA

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