An O(sqrt(n)) space bound for obstruction-free leader election

Abstract : We present a deterministic obstruction-free implementation of leader election from $O(\sqrt n)$ atomic $O(\log n)$-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 (2012), to obtain a fast randomized leader election (and thus test-and-set) implementation from $O(\sqrt n)$ $O(\log n)$-bit registers, that has expected step complexity $O(\log^\ast n)$ against the oblivious adversary. Our algorithm provides the first sub-linear space upper bound for obstruction-free leader election. A lower bound of $\Omega(\log n)$ has been known since 1989. 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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Submitted on : Monday, October 21, 2013 - 12:31:10 PM
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George Giakkoupis, Maryam Helmi, Lisa Higham, Philipp Woelfel. An O(sqrt(n)) space bound for obstruction-free leader election. DISC - 27th International Symposium on Distributed Computing, Oct 2013, Jerusalem, Israel. ⟨hal-00875167⟩

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