Time-and Space-eecient Randomized Consensus

A protocol is presented which solves the randomized consensus problem9] for shared memory. The protocol uses a total of O(p 2 +n) worst-case expected increment, decrement and read operations on a set of three shared O(log n)-bit counters, where p is the number of active processors and n is the total number of processors. It requires less space than previous polynomial-time consensus protocolss6, 7], and is faster when not all of the processors participate in the protocol. A modiied version of the protocol yields a weak shared coin whose bias is guaranteed to be in the range 1=2 regardless of scheduler behavior, and which is the rst such protocol for the shared-memory model to guarantee that all processors agree on the outcome of the coin.