A time-randomness tradeoff for communication complexity

Abstract

We present a tight tradeoff between the expected communication complexity $\bar C$and the number R of random bits used by any Las Vegas protocol (for a two-processor system) for the list-disjointness function of two lists of n numbers of n bits each. This function evaluates to 1 if and only if the two lists correspond in at least one position. We show a log(n ²/$\bar C$) lower bound on the number of random bits used by any Las Vegas protocol, Ω(n) ≤ $\bar C$≤ O(n ²). We also show that expected communication complexity $\bar C$, Ω(n log n) ≤ $\bar C$≤ O(n ²), can be achieved using no more than (1+o(1)) log(n ²/$\bar C$) random bits.

This work was supported by the DFG, SFB 124, TP B2, VLSI-Entwurf und Parallelität and ESPRIT P3075 ALCOM