Tight bounds for synchronous communication of information using bits and silence

• Published in: Discrete Applied Mathematics Vol. 129; no. 1; pp. 195 - 209
• Main Authors: O'Reilly, Una-May, Santoro, Nicola
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.06.2003
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/S0166-218X(02)00240-8

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 protocols whose bit-time complexity match the ones expressed by the lower bounds. We actually show that the algorithms are 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 relabeling). Similar results are derived when transmissions are subject to corruptions. In these results, the number of bits is a priori agreed upon. We also derive lower bounds on the worst case complexity of two-party communication when the number of bits is variable; the bounds prove that any improvement would be by an additive constant (even in presence of an oracle).