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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References
Afek, Y., Attiya, H., Dolev, D., Gafni, E., Merritt, M., Shavit, N.: Atomic snapshots of shared memory. J. of the ACM 40(4), 873–890 (1993)
Afek, Y., Gafni, E., Tromp, J., Vitányi, P.: Wait-free test-and-set. In: Segall, A., Zaks, S. (eds.) WDAG 1992. LNCS, vol. 647, pp. 85–94. Springer, Heidelberg (1992)
Alistarh, D., Aspnes, J.: Sub-logarithmic test-and-set against a weak adversary. In: Peleg, D. (ed.) DISC. LNCS, vol. 6950, pp. 97–109. Springer, Heidelberg (2011)
Alistarh, D., Aspnes, J., Censor-Hillel, K., Gilbert, S., Zadimoghaddam, M.: Optimal-time adaptive strong renaming, with applications to counting. In: Proc. of 30th PODC, pp. 239–248 (2011)
Alistarh, D., Aspnes, J., Gilbert, S., Guerraoui, R.: The complexity of renaming. In: Proc. of 52nd FOCS, pp. 718–727 (2011)
Alistarh, D., Attiya, H., Gilbert, S., Giurgiu, A., Guerraoui, R.: Fast randomized test-and-set and renaming. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 94–108. Springer, Heidelberg (2010)
Anderson, J.H.: Composite registers. Dist. Comp. 6(3), 141–154 (1993)
Aspnes, J.: Randomized consensus in expected o(n 2) total work using single-writer registers. In: Peleg, D. (ed.) DISC. LNCS, vol. 6950, pp. 363–373. Springer, Heidelberg (2011)
Aspnes, J.: Faster randomized consensus with an oblivious adversary. In: Proc. of 31st PODC, pp. 1–8 (2012)
Aspnes, J.: A modular approach to shared-memory consensus, with applications to the probabilistic-write model. Dist. Comp. 25(2), 179–188 (2012)
Attiya, H., Censor, K.: Tight bounds for asynchronous randomized consensus. J. of the ACM 55(5) (2008)
Attiya, H., Censor-Hillel, K.: Lower bounds for randomized consensus under a weak adversary. SIAM J. on Comp. 39(8), 3885–3904 (2010)
Aumann, Y.: Efficient asynchronous consensus with the weak adversary scheduler. In: Proc. of 16th PODC, pp. 209–218 (1997)
Buhrman, H., Panconesi, A., Silvestri, R., Vitányi, P.: On the importance of having an identity or, is consensus really universal? Dist. Comp. 18(3), 167–176 (2006)
Eberly, W., Higham, L., Warpechowska-Gruca, J.: Long-lived, fast, waitfree renaming with optimal name space and high throughput. In: Kutten, S. (ed.) DISC 1998. LNCS, vol. 1499, pp. 149–160. Springer, Heidelberg (1998)
Ellen, F., Fatourou, P., Ruppert, E.: Time lower bounds for implementations of multi-writer snapshots. J. of the ACM 54(6) (2007)
Ellen, F., Fatourou, P., Ruppert, E.: The space complexity of unbounded timestamps. Dist. Comp. 21(2), 103–115 (2008)
Fich, F., Herlihy, M., Shavit, N.: On the space complexity of randomized synchronization. J. of the ACM 45(5), 843–862 (1998)
Fich, F.E., Luchangco, V., Moir, M., Shavit, N.N.: Obstruction-free algorithms can be practically wait-free. In: Fraigniaud, P. (ed.) DISC 2005. LNCS, vol. 3724, pp. 78–92. Springer, Heidelberg (2005)
Fischer, M., Lynch, N., Paterson, M.: Impossibility of distributed consensus with one faulty process. J. of the ACM 32(2), 374–382 (1985)
Giakkoupis, G., Woelfel, P.: On the time and space complexity of randomized test-and-set. In: Proc. of 31st PODC, pp. 19–28 (2012)
Golab, W., Hendler, D., Woelfel, P.: An O(1) RMRs leader election algorithm. SIAM J. on Comp. 39, 2726–2760 (2010)
Helmi, M., Higham, L., Pacheco, E., Woelfel, P.: The space complexity of long-lived and one-shot timestamp implementations. In: Proc. of 30th PODC, pp. 139–148 (2011)
Herlihy, M.: Wait-free synchronization. ACM Trans. Program. Lang. Syst. 13(1), 124–149 (1991)
Jayanti, P., Tan, K., Toueg, S.: Time and space lower bounds for nonblocking implementations. SIAM J. on Comp. 30(2), 438–456 (2000)
Kruskal, C., Rudolph, L., Snir, M.: Efficient synchronization on multiprocessors with shared memory. ACM Trans. Program. Lang. Syst. 10(4), 579–601 (1988)
McDiarmid, C.: Concentration. In: Habib, M., McDiarmid, C., Ramirez-Alfonsin, J., Reed, B. (eds.) Probabilistic Methods for Algorithmic Discrete Mathematics, pp. 195–248. Springer (1998)
Panconesi, A., Papatriantafilou, M., Tsigas, P., Vitányi, P.: Randomized naming using wait-free shared variables. Dist. Comp. 11(3), 113–124 (1998)
Styer, E., Peterson, G.: Tight bounds for shared memory symmetric mutual exclusion problems. In: Proc. of 8th PODC, pp. 177–191 (1989)
Tromp, J., Vitányi, P.: Randomized two-process wait-free test-and-set. Dist. Comp. 15(3), 127–135 (2002)
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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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