Multiparty Communication Complexity: Very Hard Functions

@inproceedings{Manuch1999MultipartyCC,
  title={Multiparty Communication Complexity: Very Hard Functions},
  author={J{\'a}n Manuch},
  booktitle={MFCS},
  year={1999}
}
  • J. Manuch
  • Published in MFCS 6 September 1999
  • Mathematics, Computer Science
We consider the multiparty communication model defined in [DF89] using the formalism from [Hr97]. First, we correct an inaccuracy in the proof of the fundamental result of [DR95] providing a lower bound on the nondeterministic communication complexity of a function. Then we construct several very hard functions, i.e., functions such that those as well as their complements have the worst possible nondeterministic communication complexity. The problem to find a particular very haxd function was… 
1 Citations
Mathematical Foundations of Computer Science 1999
Let /? be a real number > 1. Addition and multiplication by a fixed positive integer of real numbers represented in bsise /3 cire shown to be computable by an on-line algorithm, and thus are

References

SHOWING 1-10 OF 11 REFERENCES
Optimal Lower Bounds on the Multiparty Communication Complexity
TLDR
The two-party method based on a crossing sequence argument introduced in [Y79] is generalized and optimal lower and upper bounds on the multiparty communication complexity of boolean functions are derived.
Determinism vs. Nondeterminism in Multiparty Communication Complexity
TLDR
It is shown that it is possible to evaluate the Boolean function deterministically with only a polynomial increase in communication and number of parties accessed with respect to the information lower bound given by the nondeterministic communication complexity of the function.
Multiparty communication complexity
  • D. Dolev, T. Feder
  • Computer Science
    30th Annual Symposium on Foundations of Computer Science
  • 1989
TLDR
It is shown that it is possible to obtain the Boolean answer deterministically with only a polynomial increase in communication with respect to the information lower bound given by the nondeterministic communication complexity of the function.
Communication Complexity
Multi-party protocols
TLDR
A new model is studied, in which a collection of processes P0, ..., Pk−1 that share information about a set of integers {a0, …,ak−1}, communicate to determine a 0-1 predicate of the numbers.
Multiparty protocols and logspace-hard pseudorandom sequences
TLDR
Lower bounds of the form &OHgr;(n</italic)·c<supscrpt>-k</supsCrpt></italic>), for the number of bits that need to be exchanged in order to compute some (explicitly given) functions in P, are proved.
Communication Complexity and Parallel Computing
  • J. Hromkovic
  • Computer Science
    Texts in Theoretical Computer Science An EATCS Series
  • 1997
TLDR
This book is written as a textbook for undergraduate and graduate students and provides a careful explanation of the subject as well as motivation for further research.
Lower Bounds on the Multiparty Communication Complexity
TLDR
The two-party method based on a crossing sequence argument introduced by Yao is extended and the power of a restricted multiparty communication model in which the coordinator is allowed to send at most one message to each party is investigated.
Communication complexity and parallel computing, An EATCS Series
  • Communication complexity and parallel computing, An EATCS Series
  • 1997
...
...