LIPIcs - Leibniz International Proceedings in Informatics. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)
Doi
Abstract
In the `Number-on-Forehead\u27 (NOF) model of multiparty communication,
the input is a k times m boolean matrix A (where k is the number of players) and Player i sees all bits except those in the i-th row, and the players communicate by broadcast in order to evaluate a specified function f at A.
We discover new computational power when k exceeds log m. We give a protocol with communication cost poly-logarithmic in m, for block composed functions with limited block width. These are functions
of the form f o g where f is a symmetric b-variate function, and g is a (kr)-variate function and (f o g)(A) is defined, for a k times (br) matrix to be f(g(A-1),...,g(A-b)) where A-i is the i-th (k times r) block of A. Our protocol works provided that k > 1+ ln b + (2 to the power of r).
Ada et al. (ICALP\u272012) previously obtained simultaneous and deterministic efficient protocols for composed functions of block-width one. The new protocol is the first to work for block composed functions with block-width greather than one. Moreover, it is simultaneous, with vanishingly small error probability, if public coin randomness is allowed. The deterministic and zero-error version barely uses interaction
