max planck institut
informatik

MPI-I-93-162

On multi-party communication complexity of random functions

Grolmusz, Vince

MPI-I-93-162. December 1993, 10 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
We prove that almost all Boolean function has a high $k$--party communication complexity. The 2--party case was settled by {\it Papadimitriou} and {\it Sipser}.
Proving the $k$--party case needs a deeper investigation of the underlying structure
of the $k$--cylinder--intersections; (the 2--cylinder--intersections are the rectangles).

\noindent First we examine the basic properties of $k$--cylinder--intersections, then an upper estimation is given for their number, which facilitates to prove the lower--bound theorem for the $k$--party communication complexity of randomly chosen Boolean functions. In the last section we extend our results to the $\varepsilon$--distributional communication complexity of random functions.
Acknowledgement:
References to related material:

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BibTeX
@TECHREPORT{Grolmusz93d,
AUTHOR = {Grolmusz, Vince},
TITLE = {On multi-party communication complexity of random functions},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},