Abstract
Obstruction-free consensus, ensuring that a process running solo will eventually terminate, is at the core of practical ways to solve consensus, e.g., by using randomization or failure detectors. An obstruction-free consensus algorithm may not terminate in many executions, but it must terminate whenever a process runs solo. Such an algorithm can be evaluated by its solo step complexity, which bounds the worst case number of steps taken by a process running alone, from any configuration, until it decides.
This paper presents a lower bound of \(\varOmega (\log n)\) on the solo step complexity of obstruction-free binary anonymous consensus. The proof constructs a sequence of executions in which more and more distinct variables are about to be written to, and then uses the backtracking covering technique to obtain a single execution in which many variables are accessed.
This work is supported by the Israel Science Foundation (grant 1749/14). The second and third authors are also supported by the Lynne and William Frankel Center for Computing Science at Ben-Gurion University.
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Notes
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Note that once a variable becomes covered in the executions we construct for our proofs, it remains covered, so a bit of \(\varPsi \) may be flipped from 1 to 0 only if the corresponding variable was read in \(\phi _i\) and is no longer read in \(\phi _{i+1}\).
References
Aspnes, J., Attiya, H., Censor-Hillel, K., Hendler, D.: Lower bounds for restricted-use objects. In: SPAA, pp. 172–181 (2012)
Aspnes, J., Ellen, F.: Tight bounds for adopt-commit objects. Theor. Comput. Syst. 55(3), 451–474 (2013)
Attiya, H., Guerraoui, R., Hendler, D., Kuznetsov, P.: The complexity of obstruction-free implementations. J. ACM 56(4), 444–468 (2009)
Bouzid, Z., Sutra, P., Travers, C.: Anonymous agreement: the janus algorithm. In: Fernà ndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 175–190. Springer, Heidelberg (2011)
Capdevielle, C., Johnen, C., Kuznetsov, P., Milani, A.: Brief announcement: on the uncontended complexity of anonymous consensus. In: Moses, Y. (ed.) DISC 2015. LNCS, vol. 9363, pp. 667–668. Springer, Heidelberg (2015)
Ellen, F., Hendler, D., Shavit, N.: On the inherent sequentiality of concurrent objects. SIAM J. Comput. 41(3), 519–536 (2012)
Fich, F., Herlihy, M., Shavit, N.: On the space complexity of randomized synchronization. J. ACM 45(5), 843–862 (1998)
Hendler, D., Shavit, N.: Solo-valency and the cost of coordination. Distrib. Comput. 21(1), 43–54 (2008)
Herlihy, M., Luchangco, V., Moir, M.: Obstruction-free synchronization: double-ended queues as an example. In: ICDCS, pp. 522–529 (2003)
Luchangco, V., Moir, M., Shavit, N.N.: On the uncontended complexity of consensus. In: Fich, F.E. (ed.) DISC 2003. LNCS, vol. 2848, pp. 45–59. Springer, Heidelberg (2003)
Zhu, L.: Brief announcement: tight space bounds for memoryless anonymous consensus. In: Moses, Y. (ed.) DISC 2015. LNCS, vol. 9363, pp. 665–666. Springer, Heidelberg (2015)
Zhu, L.: A tight space bound for consensus. In: STOC (2016, to appear)
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Attiya, H., Ben-Baruch, O., Hendler, D. (2016). Lower Bound on the Step Complexity of Anonymous Binary Consensus. In: Gavoille, C., Ilcinkas, D. (eds) Distributed Computing. DISC 2016. Lecture Notes in Computer Science(), vol 9888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53426-7_19
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