The expressiveness of silence: Bounds for synchronous communication of information using bits and silence

Abstract

We establish worst-case and average-case lower bounds on the trade-off between the time and bit complexity for two-party communication in synchronous networks. We prove that the bounds are tight by presenting a protocol which has bit-time complexity matching the ones expressed by the lower bounds. We actually show that the algorithm is everywhere optimal: at any point of the trade-off and for any universe of data to be communicated, no other solution has better complexity to communicate any element of that universe (within a fixed relabelling). Similar results are derived when transmissions are subject to corruptions.