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

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2012, RANDOM 2012)

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

Work supported in part by NSF Grant IIS-0916565.

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Authors and Affiliations

  1. Department of Computer Science, Dartmouth College, Hanover, NH, 03755, USA

    Amit Chakrabarti, Ranganath Kondapally & Zhenghui Wang

Authors
  1. Amit Chakrabarti
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  2. Ranganath Kondapally
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  3. Zhenghui Wang
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Carnegie Mellon University, Gates Building 7203, 15213, Pittsburgh, PA, USA

    Anupam Gupta

  2. Department of Computer Science, University Kiel, Olshausenstraße 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Centre Universitaire d’Informatique, University of Geneva, Battelle A, 7 route de Drize, 1227, Carouge, Switzerland

    José Rolim

  4. Department of Computer Science, Foundation School of Engineering and Applied Science, Columbia University, Amsterdam Avenue 1214, 10027-7003, New York, NY, USA

    Rocco Servedio

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Chakrabarti, A., Kondapally, R., Wang, Z. (2012). Information Complexity versus Corruption and Applications to Orthogonality and Gap-Hamming. In: Gupta, A., Jansen, K., Rolim, J., Servedio, R. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2012 2012. Lecture Notes in Computer Science, vol 7408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32512-0_41

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  • DOI: https://doi.org/10.1007/978-3-642-32512-0_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32511-3

  • Online ISBN: 978-3-642-32512-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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