Silence-based communication

Anand K. Dhulipala, Christina Fragouli, Alon Orlitsky

Abstract: Communication complexity - the minimum amount of communication required - for computing a function of data held by several parties is studied. A communication model where silence is used to convey information is introduced. For this model the worst case and average-case complexities of symmetric functions are studied. For binary-input functions the average- and worst case complexities are determined and the protocols achieving them are described. For functions of nonbinary inputs one-round communication, where each party is restricted to communicate in consecutive stages, is considered and the extra amount of communication required by one- over multiple-round communication is analyzed. For the special case of ternary-input functions close lower and upper bounds on the worst case one-round complexity are provided and protocols achieving them are described. Protocols achieving the average-case one-round complexity for ternary-input functions are also described. These protocols can be generalized to inputs of arbitrary size.