Determinism vs. nondeterminism in multiparty communication complexity

A given Boolean function has its input distributed among many parties. The aim is to determine which parties to talk to and what information to exchange in order to evaluate the function while minimizing the total communication. This paper shows 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.