Group mutual exclusion in O(log n) RMR

We present an algorithm to solve the group mutual exclusion, problem in the cache-coherent (CC) model. For the same problem in the distributed shared memory (DSM) model, Danek and Hadzilacos presented algorithms of O(n) remote memory references (RMR) and proved a matching lower bound, where n is the number of processes. We show that in the CC model, using registers and LL/SC variables, our algorithm achieves O(min(log n,k)) RMR, where k is the point contention, which is so far the best. Moreover, given a recent result of Attiya, Hendler and Woelfel showing that exclusion problems have a Ω(log n) RME lower bound using registers, comparison primitives and LL/SC variables, our algorithm thus achieves the best theoretical bound.