Abstract
We present a deterministic obstruction-free implementation of leader election from \(O(\sqrt n)\) atomic O(logn)-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 Woelfel [21], to obtain a fast randomized leader election (and thus test-and-set) implementation from \(O(\sqrt n)\) O(logn)-bit registers, that has expected step complexity O(log ∗ n) against the oblivious adversary.
Our algorithm provides the first sub-linear space upper bound for obstruction-free leader election. A lower bound of Ω(logn) has been known since 1989 [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.
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Giakkoupis, G., Helmi, M., Higham, L., Woelfel, P. (2013). An \(O(\sqrt n)\) Space Bound for Obstruction-Free Leader Election. In: Afek, Y. (eds) Distributed Computing. DISC 2013. Lecture Notes in Computer Science, vol 8205. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41527-2_4
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