Affiliation:
1. Microsoft Research Cambridge, Cambridge, UK
2. Yale, New Haven, CT
3. Technion, Haifa, Israel
4. National University of Singapore, Singapore
5. EPFL, Lausanne, Switzerland
Abstract
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(
k
log (
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.
Funder
Division of Computing and Communication Foundations
Ministry of Education - Singapore
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
14 articles.
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1. Randomized consensus with regular registers;Information Processing Letters;2022-03
2. On Register Linearizability and Termination;Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing;2021-07-21
3. Randomized renaming in shared memory systems;Journal of Parallel and Distributed Computing;2021-04
4. Efficiency Guarantees for Parallel Incremental Algorithms under Relaxed Schedulers;The 31st ACM Symposium on Parallelism in Algorithms and Architectures;2019-06-17
5. Distributionally Linearizable Data Structures;Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures;2018-07-11