Alistarh, Dan-AdrianIST Austria; Aspnes, James; Censor Hillel, Keren; Gilbert, Seth; Guerraoui, Rachid
This article presents the first tight bounds on the time complexity of shared-memory renaming, a fundamental problem in distributed computing in which a set of processes need to pick distinct identifiers from a small namespace. We first prove an individual lower bound of ω(k) process steps for deterministic renaming into any namespace of size subexponential in k, where k is the number of participants. The bound is tight: it draws an exponential separation between deterministic and randomized solutions, and implies new tight bounds for deterministic concurrent fetch-and-increment counters, queues, and stacks. The proof is based on a new reduction from renaming to another fundamental problem in distributed computing: mutual exclusion. We complement this individual bound with a global lower bound of ω(klog(k/c)) on the total step complexity of renaming into a namespace of size ck, for any c = 1. This result applies to randomized algorithms against a strong adversary, and helps derive new global lower bounds for randomized approximate counter implementations, that are tight within logarithmic factors. On the algorithmic side, we give a protocol that transforms any sorting network into a randomized strong adaptive renaming algorithm, with expected cost equal to the depth of the sorting network. This gives a tight adaptive renaming algorithm with expected step complexity O(log k), where k is the contention in the current execution. This algorithm is the first to achieve sublinear time, and it is time-optimal as per our randomized lower bound. Finally, we use this renaming protocol to build monotone-consistent counters with logarithmic step complexity and linearizable fetch-and-increment registers with polylogarithmic cost.
Journal of the ACM
The work of J. Aspnes was supported in part by NSF grant CCF-0916389. The work of S. Gilbert was supported by Singapore AcRF-2 MOE 2011-T2-2-042. K. Censor-Hillel is a Shalon Fellow. Part of this work was performed while K. Censor-Hillel was a postdoc at MIT, supported by the Simons Postdoctoral Fellowship.
Alistarh D-A, Aspnes J, Censor Hillel K, Gilbert S, Guerraoui R. Tight bounds for asynchronous renaming. Journal of the ACM. 2014;61(3). doi:10.1145/2597630
Alistarh, D.-A., Aspnes, J., Censor Hillel, K., Gilbert, S., & Guerraoui, R. (2014). Tight bounds for asynchronous renaming. Journal of the ACM. ACM. https://doi.org/10.1145/2597630
Alistarh, Dan-Adrian, James Aspnes, Keren Censor Hillel, Seth Gilbert, and Rachid Guerraoui. “Tight Bounds for Asynchronous Renaming.” Journal of the ACM. ACM, 2014. https://doi.org/10.1145/2597630.
D.-A. Alistarh, J. Aspnes, K. Censor Hillel, S. Gilbert, and R. Guerraoui, “Tight bounds for asynchronous renaming,” Journal of the ACM, vol. 61, no. 3. ACM, 2014.
Alistarh D-A, Aspnes J, Censor Hillel K, Gilbert S, Guerraoui R. 2014. Tight bounds for asynchronous renaming. Journal of the ACM. 61(3).
Alistarh, Dan-Adrian, et al. “Tight Bounds for Asynchronous Renaming.” Journal of the ACM, vol. 61, no. 3, ACM, 2014, doi:10.1145/2597630.