Alistarh, Dan-AdrianISTA; Aspnes, James; Gilbert, Seth; Guerraoui, Rachid
We study the complexity of renaming, a fundamental problem in distributed computing in which a set of processes need to pick distinct names from a given namespace. We prove an individual lower bound of Ω(k) process steps for deterministic renaming into any namespace of size sub-exponential in k, where k is the number of participants. This bound is tight: it draws an exponential separation between deterministic and randomized solutions, and implies new tight bounds for deterministic fetch-and-increment registers, queues and stacks. The proof of the bound is interesting in its own right, for it relies on the first reduction from renaming to another fundamental problem in distributed computing: mutual exclusion. We complement our individual bound with a global lower bound of Ω(k log (k/c)) on the total step complexity of renaming into a namespace of size ck, for any c ≥ 1. This applies to randomized algorithms against a strong adversary, and helps derive new global lower bounds for randomized approximate counter and fetch-and-increment implementations, all tight within logarithmic factors.
The authors would like to thank Hagit Attiya and Keren Censor-Hillel for discussions and feedback on earlier versions of this paper, and the anonymous reviewers for their very useful suggestions.
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FOCS: Foundations of Computer Science
Alistarh D-A, Aspnes J, Gilbert S, Guerraoui R. The complexity of renaming. In: IEEE; 2011:718-727. doi:10.1109/FOCS.2011.66
Alistarh, D.-A., Aspnes, J., Gilbert, S., & Guerraoui, R. (2011). The complexity of renaming (pp. 718–727). Presented at the FOCS: Foundations of Computer Science, IEEE. https://doi.org/10.1109/FOCS.2011.66
Alistarh, Dan-Adrian, James Aspnes, Seth Gilbert, and Rachid Guerraoui. “The Complexity of Renaming,” 718–27. IEEE, 2011. https://doi.org/10.1109/FOCS.2011.66.
D.-A. Alistarh, J. Aspnes, S. Gilbert, and R. Guerraoui, “The complexity of renaming,” presented at the FOCS: Foundations of Computer Science, 2011, pp. 718–727.
Alistarh D-A, Aspnes J, Gilbert S, Guerraoui R. 2011. The complexity of renaming. FOCS: Foundations of Computer Science, 718–727.
Alistarh, Dan-Adrian, et al. The Complexity of Renaming. IEEE, 2011, pp. 718–27, doi:10.1109/FOCS.2011.66.