We consider the problem of simulating a k-valued register in a wait-
free manner using binary registers as building blocks, where k > 2.
We show that for any simulation using atomic binary base registers
to simulate a safe k-valued register in which the read algorithm
takes the optimal number of steps (log_2 k), the write algorithm
must take at least log k steps in the worst case. A fortiori, the same
lower bound applies when the simulated register should be regular. Previously known algorithms show that both these lower bounds are tight. We also show that in order to simulate an atomic k -valued register for two readers, the optimal number of steps for the read algorithm must be strictly larger than log_2 k.
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Consensus with Max Registers
We consider the problem of implementing randomized wait-free consensus from max registers under the assumption of an oblivious adversary. We show that max registers solve m-valued consensus for arbitrary m in expected O(log^* n) steps per process, beating the Omega(log m/log log m) lower bound for ordinary registers when m is large and the best previously known O(log log n) upper bound when m is small. A simple max-register implementation based on double-collect snapshots translates this result into an O(n log n) expected step implementation of m-valued consensus from n single-writer registers, improving on the best previously-known bound of O(n log^2 n) for single-writer registers.
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- NSF-PAR ID:
- 10120845
- Date Published:
- Journal Name:
- Leibniz international proceedings in informatics
- Volume:
- 146
- ISSN:
- 1868-8969
- Page Range / eLocation ID:
- 1:1-1:9
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/http://dx.doi.org/10.4230/LIPIcs.DISC.2019.1
