Lower bounds for randomized mutual exclusion

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 Ω(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 shared variable. Our lower bounds rely on an analysis of Markov chains that may be of interest on its own and may have applications elsewhere.

Original languageEnglish
Pages (from-to)1550-1563
Number of pages14
JournalSIAM Journal on Computing
Issue number6
StatePublished - Dec 1998


  • Lower bounds
  • Markov chains
  • Mutual exclusion
  • Randomized distributed algorithms


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