# On the time and space complexity of randomized test-and-set

1 ASAP - As Scalable As Possible: foundations of large scale dynamic distributed systems
IRISA-D1 - SYSTÈMES LARGE ÉCHELLE, Inria Rennes – Bretagne Atlantique
Abstract : We study the time and space complexity of randomized Test-And-Set (TAS) implementations from atomic read/write registers in asynchronous shared memory models with $n$ processes. We present an adaptive TAS algorithm with an expected (individual) step complexity of $O(\log^\ast k)$, for contention $k$, against the oblivious adversary, improving a previous (non-adaptive) upper bound of $O(\log\log n)$ (Alistarh and Aspnes, 2011). We also present a modified version of the adaptive RatRace TAS algorithm (Alistarh et al., 2010), which improves the space complexity from $O(n^3)$ to $O(n)$, while maintaining logarithmic expected step complexity against the adaptive adversary. We complement this upper bound with an $\Omega(\log n)$ lower bound on the space complexity of any TAS algorithm that has the nondeterministic solo-termination property (which is a weaker progress condition than wait-freedom). No non-trivial lower bounds on the space requirements of TAS were known prior to this work.
Document type :
Conference papers

Cited literature [14 references]

https://hal.inria.fr/hal-00722947
Contributor : George Giakkoupis <>
Submitted on : Monday, August 6, 2012 - 5:07:44 PM
Last modification on : Wednesday, June 16, 2021 - 3:42:08 AM
Long-term archiving on: : Wednesday, November 7, 2012 - 3:22:53 AM

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podc2012_tas.pdf
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• HAL Id : hal-00722947, version 1

### Citation

George Giakkoupis, Philipp Woelfel. On the time and space complexity of randomized test-and-set. PODC - 31st Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, Jul 2012, Madeira, Portugal. ⟨hal-00722947⟩

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