Bounds on tradeoffs between randomness and communication complexity

Ran Canetti*, Oded Goldreich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The power of randomness in improving the efficiency (or even possibility) of computations has been demonstrated in numerous contexts. A fundamental question is how much randomness is required for these improvements, or how does the improvement grow as a function of the amount of randomness allowed. This quantitative question, restricted to the context of communication complexity, is the focus of our paper. We prove general lower bounds on the amount of randomness used in randomized protocols for computing a function f, the input of which is split between two parties. The bounds depend on the number of bits communicated and the deterministic communication complexity of f. Four models for communication complexity are considered: the random input of the parties may be public or private, and the communication may be one-way or two-way. (Unbounded advantage is allowed.) The bounds are shown to be tight; i.e., we demonstrate functions and protocols for these functions which meet the above bounds up to a constant factor. We do this for all the models, for all values of the deterministic communication complexity, and for all possible quantities of bits communicated.

Original languageEnglish
Pages (from-to)141-167
Number of pages27
JournalComputational Complexity
Volume3
Issue number2
DOIs
StatePublished - Jun 1993
Externally publishedYes

Keywords

  • Communication Complexity
  • Complexity-Randomness tradeoff
  • Lower bounds
  • Randomized Computation
  • Subject classifications: 68Q22
  • protocols

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