Faster approximate agreement with multi-writer registers

We consider the complexity of the wait-free approximate agreement problem in an asynchronous shared memory comprised of only single-bit multi-writer multi-reader registers. For real-valued inputs x₁,...,x_n and ε we show matching upper and lower bounds of Θ(log(max{|x₁|,...,|x_n|}/ε)) steps and shared registers. For inputs drawn from any fixed range this is significantly better than the best possible algorithm for single-writer multi-reader registers, which requires Ω(logn) rounds. This implies a separation between the wait-free single-writer multi-reader and wait-free multi-writer multi-reader models of computation