Communication with contextual uncertainty

Badih Ghazi, Han Komargodski, Pravesh Kothari, Madhu Sudan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

We introduce a simple model illustrating the role of context in communication and the challenge posed by uncertainty of knowledge of context. We consider a variant of distributional communication complexity where Alice gets some information x and Bob gets y, where (x, y) is drawn from a known distribution, and Bob wishes to compute some function g(x, y) (with high probability over (x, y)). In our variant, Alice does not know g, but only knows some function/which is an approximation of g. Thus, the function being computed forms the context for the communication, and knowing it imperfectly models (mild) uncertainty in this context. A naive solution would be for Alice and Bob to first agree on some common function h that is close to both/and g and then use a protocol for h to compute h(x, y). We show that any such agreement leads to a large overhead in communication ruling out such a universal solution. In contrast, we show that if g has a one-way communication protocol with complexity k in the standard setting, then it has a communication protocol with complexity 0(k (1 +/)) in the uncertain setting, where/denotes the mutual information between x and y. In the particular case where the input distribution is a product distribution, the protocol in the uncertain setting only incurs a constant factor blow-up in communication and error. Furthermore, we show that the dependence on the mutual information/is required. Namely, we construct a class of functions along with a non-product distribution over (x, y) for which the communication complexity is a single bit in the standard setting but at least Q, (<Jn) bits in the uncertain setting.

Original languageEnglish (US)
Title of host publication27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
EditorsRobert Krauthgamer
PublisherAssociation for Computing Machinery
Pages2072-2085
Number of pages14
ISBN (Electronic)9781510819672
DOIs
StatePublished - Jan 1 2016
Event27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 - Arlington, United States
Duration: Jan 10 2016Jan 12 2016

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume3

Other

Other27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
CountryUnited States
CityArlington
Period1/10/161/12/16

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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  • Cite this

    Ghazi, B., Komargodski, H., Kothari, P., & Sudan, M. (2016). Communication with contextual uncertainty. In R. Krauthgamer (Ed.), 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 (pp. 2072-2085). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 3). Association for Computing Machinery. https://doi.org/10.1137/1.9781611974331.ch144