An $O\sqrt n$ Space Bound for Obstruction-Free Leader Election

We present a deterministic obstruction-free implementation of leader election from $O\sqrt n$ atomic Ologn-bit registers in the standard asynchronous shared memory system with n processes. We provide also a technique to transform any deterministic obstruction-free algorithm, in which any process can finish if it runs for b steps without interference, into a randomized wait-free algorithm for the oblivious adversary, in which the expected step complexity is polynomial in n and b. This transformation allows us to combine our obstruction-free algorithm with the leader election algorithm by Giakkoupis and Woelfeli¾?[21], to obtain a fast randomized leader election and thus test-and-set implementation from $O\sqrt n$ Ologn-bit registers, that has expected step complexity Ologi¾? n against the oblivious adversary. Our algorithm provides the first sub-linear space upper bound for obstruction-free leader election. A lower bound of Ωlogn has been known since 1989i¾?[29]. Our research is also motivated by the long-standing open problem whether there is an obstruction-free consensus algorithm which uses fewer than n registers.