License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.465
URN: urn:nbn:de:0030-drops-47174
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4717/
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Blais, Eric ; Brody, Joshua ; Ghazi, Badih

The Information Complexity of Hamming Distance

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Abstract

The Hamming distance function Ham_{n,d} returns 1 on all pairs of inputs x and y that differ in at most d coordinates and returns 0 otherwise. We initiate the study of the information complexity of the Hamming distance function.

We give a new optimal lower bound for the information complexity of the Ham_{n,d} function in the small-error regime where the protocol is required to err with probability at most epsilon < d/n. We also give a new conditional lower bound for the information complexity of Ham_{n,d} that is optimal in all regimes. These results imply the first new lower bounds on the communication complexity of the Hamming distance function for the shared randomness two-way communication model since Pang and El-Gamal (1986). These results also imply new lower bounds in the areas of property testing and parity decision tree complexity.

BibTeX - Entry

@InProceedings{blais_et_al:LIPIcs:2014:4717,
  author =	{Eric Blais and Joshua Brody and Badih Ghazi},
  title =	{{The Information Complexity of Hamming Distance}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{465--489},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and Nikhil R. Devanur and Cristopher Moore},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4717},
  URN =		{urn:nbn:de:0030-drops-47174},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.465},
  annote =	{Keywords: Hamming distance, communication complexity, information complexity}
}

Keywords: Hamming distance, communication complexity, information complexity
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)
Issue Date: 2014
Date of publication: 04.09.2014

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