Journal of Algorithms
Private vs. common random bits in communication complexity
Information Processing Letters
Determinism vs. nondeterminism in multiparty communication complexity
SIAM Journal on Computing
Amortized Communication Complexity
SIAM Journal on Computing
A comparison of two lower-bound methods for communication complexity
MFCS '94 Selected papers from the 19th international symposium on Mathematical foundations of computer science
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Approximate counting of inversions in a data stream
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Multiparty communication complexity of vector---valued and sum---type functions
Information Theory, Combinatorics, and Search Theory
Hi-index | 5.23 |
Consider the ''Number in Hand'' multiparty communication complexity model, where k players holding inputs x"1,...,x"k@?{0,1}^n communicate to compute the value f(x"1,...,x"k) of a function f known to all of them. The main lower bound technique for the communication complexity of such problems is that of partition arguments: partition the k players into two disjoint sets of players and find a lower bound for the induced two-party communication complexity problem. In this paper, we study the power of partition arguments. Our two main results are very different in nature: (i)For randomized communication complexity, we show that partition arguments may yield bounds that are exponentially far from the true communication complexity. Specifically, we prove that there exists a 3-argument function f whose communication complexity is @W(n), while partition arguments can only yield an @W(logn) lower bound. The same holds for nondeterministiccommunication complexity. (ii)For deterministic communication complexity, we prove that finding significant gaps between the true communication complexity and the best lower bound that can be obtained via partition arguments, would imply progress on a generalized version of the ''log-rank conjecture'' in communication complexity. We also observe that, in the case of computing relations (search problems), very large gaps do exist. We conclude with two results on the multiparty ''fooling set technique'', another method for obtaining communication complexity lower bounds.