Corpus ID: 18366641

A quadratically tight partition bound for classical communication complexity and query complexity

@article{Jain2014AQT,
  title={A quadratically tight partition bound for classical communication complexity and query complexity},
  author={R. Jain and T. Lee and N. Vishnoi},
  journal={ArXiv},
  year={2014},
  volume={abs/1401.4512}
}
  • R. Jain, T. Lee, N. Vishnoi
  • Published 2014
  • Mathematics, Computer Science
  • ArXiv
  • In this work we introduce, both for classical communication complexity and query complexity, a modification of the 'partition bound' introduced by Jain and Klauck [2010]. We call it the 'public-coin partition bound'. We show that (the logarithm to the base two of) its communication complexity and query complexity versions form, for all relations, a quadratically tight lower bound on the public-coin randomized communication complexity and randomized query complexity respectively. 

    Topics from this paper.

    Randomized Communication vs. Partition Number
    43
    Communication Lower Bounds via Query Complexity
    1
    Relative Discrepancy Does Not Separate Information and Communication Complexity
    9
    Exponential Separation of Information and Communication for Boolean Functions
    29
    Separating decision tree complexity from subcube partition complexity
    8
    A Composition Theorem for Conical Juntas
    17

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    A Communication protocol to realize a partition Let {R 1 , R 2 , . . . , R m } be a partition of X × Y. Let x and y be the inputs to Alice and Bob respectively
      A quadratically tight partition bound ...B QUERY PROTOCOL TO REALIZE A PARTITION
        A s } be a partition of {0, 1} n such that |A i | ≤ m for each i ∈ [s]. Let x be the string in the database
          Alice queries the bits of x corresponding to A 1 . If the bits revealed are consistent with A 1 then she considers A 1 as desired assignment and stops
            B Query protocol to realize a partition
              We note that the number of such rounds is at most m and in each round at most m bits are revealed. Hence the total number of queries is at most m 2