Lower bounds for randomized mutual exclusion

Eyal Kushilevitz; Yishay Mansour; Michael O. Rabin; David Zuckerman

doi:10.1145/167088.167139

Lower bounds for randomized mutual exclusion

Eyal Kushilevitz
, Yishay Mansour
, Michael O. Rabin
, David Zuckerman

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

We establish, for the first time, lower bounds for randomized mutual-exclusion algorithms (with a read-modify-write operation). Our main result is that a constant size shared-variable cannot guarantee strong fairness, even if randomization is allowed. In fact, we prove a lower bound of fl(log log n) bits on the size of the shared-variable, which is also tight. We investigate weaker fairness conditions and derive tight (upper and lower) bounds for them as well. Surprisingly, it turns out that slightly weakening the fairness condition results in an exponential reduction in the size of the required share-variable. Our lower bounds rely on an analysis of Markov-chains, which might be interesting on its own, and may be useful for other applications.

Original language	English
Title of host publication	Proceedings of the 25th Annual ACM Symposium on Theory of Computing, STOC 1993
Publisher	Association for Computing Machinery
Pages	154-163
Number of pages	10
ISBN (Electronic)	0897915917
DOIs	https://doi.org/10.1145/167088.167139
State	Published - 1 Jun 1993
Event	25th Annual ACM Symposium on Theory of Computing, STOC 1993 - San Diego, United States Duration: 16 May 1993 → 18 May 1993

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
Volume	Part F129585
ISSN (Print)	0737-8017

Conference

Conference	25th Annual ACM Symposium on Theory of Computing, STOC 1993
Country/Territory	United States
City	San Diego
Period	16/05/93 → 18/05/93

Bibliographical note

Publisher Copyright:
© 1993 ACM.

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10.1145/167088.167139

Cite this

Kushilevitz, E., Mansour, Y., Rabin, M. O., & Zuckerman, D. (1993). Lower bounds for randomized mutual exclusion. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing, STOC 1993 (pp. 154-163). (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. Part F129585). Association for Computing Machinery. https://doi.org/10.1145/167088.167139

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title = "Lower bounds for randomized mutual exclusion",

abstract = "We establish, for the first time, lower bounds for randomized mutual-exclusion algorithms (with a read-modify-write operation). Our main result is that a constant size shared-variable cannot guarantee strong fairness, even if randomization is allowed. In fact, we prove a lower bound of fl(log log n) bits on the size of the shared-variable, which is also tight. We investigate weaker fairness conditions and derive tight (upper and lower) bounds for them as well. Surprisingly, it turns out that slightly weakening the fairness condition results in an exponential reduction in the size of the required share-variable. Our lower bounds rely on an analysis of Markov-chains, which might be interesting on its own, and may be useful for other applications.",

author = "Eyal Kushilevitz and Yishay Mansour and Rabin, \{Michael O.\} and David Zuckerman",

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Kushilevitz, E, Mansour, Y, Rabin, MO & Zuckerman, D 1993, Lower bounds for randomized mutual exclusion. in Proceedings of the 25th Annual ACM Symposium on Theory of Computing, STOC 1993. Proceedings of the Annual ACM Symposium on Theory of Computing, vol. Part F129585, Association for Computing Machinery, pp. 154-163, 25th Annual ACM Symposium on Theory of Computing, STOC 1993, San Diego, United States, 16/05/93. https://doi.org/10.1145/167088.167139

Lower bounds for randomized mutual exclusion. / Kushilevitz, Eyal; Mansour, Yishay; Rabin, Michael O. et al.
Proceedings of the 25th Annual ACM Symposium on Theory of Computing, STOC 1993. Association for Computing Machinery, 1993. p. 154-163 (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. Part F129585).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Lower bounds for randomized mutual exclusion

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