Cooperative sharing and asynchronous consensus using single-reader single-writer registers

We consider the problem of asynchronous consensus in the shared memory setting with single-reader/single-writer registers. This setting can also be viewed as a message-passing setting where there are no delays or failures of links. We provide a consensus procedure that completes in O(n log n exp(2√ln n ln(c log n log* n))) expected total work, for some constant c, assuming the value oblivious adversary scheduler. In particular, the total work is less than O(n^1+ε) for any ε. Total work is defined as the total number of operations performed by all processors collectively, including busy-waiting. The solution is based on a new algorithm for a primitive which we call cooperative-sharing. In the cooperative-sharing primitive, initially each processor has a private value and the outcome is that there is at least one input value which becomes known to all processors. We provide a new algorithm for the cooperative sharing in the single-reader/single-writer setting which completes in O(n exp(2√ln n ln(c log n log* n))) work.