An Almost Tight RMR Lower Bound for Abortable Test-And-Set
Aryaz Eghbali, Philipp Woelfel · arXiv (Cornell University) · 2018
We prove a lower bound of Omega(log n/log log n) for the remote memory reference (RMR) complexity of abortable test-and-set (leader election) in the cache-coherent (CC) and the distributed shared memory (DSM) model. This separates the complexities of abortable and non-abortable test-and-set, as the latter has constant RMR complexity [Wojciech Golab et al., 2010]. Golab, Hendler, Hadzilacos and Woelfel [Wojciech M. Golab et al., 2012] showed that compare-and-swap can be implemented from registers and test-and-set objects with constant RMR complexity. We observe that a small modification to that implementation is abortable, provided that the used test-and-set objects are atomic (or abortable). As a consequence, using existing efficient randomized wait-free implementations of test-and-set [George Giakkoupis and Philipp Woelfel, 2012], we obtain randomized abortable compare-and-swap objects with almost constant (O(log^* n)) RMR complexity.