Using Delays to Improve RMR Time Complexity in Mutual Exclusion Algorithms

We consider the time complexity of shared-memory mutual exclusion algorithms under the remote-memory-reference (RMR)time measure. In particular, algorithms based on reads, writes, and comparison primitives are considered. For such algorithms,a lower bound of Ω(log N/ log log N) RMRs per critical-section entry has been established in previous work, where N is thenumber of processes. Also, algorithms with O(log N) time complexity are known. Thus, for algorithms in this class, logarithmicor near-logarithmic RMR time complexity is fundamentally required. In this paper, we consider the question of whether better RMR time complexity is attainable if processes have the abilityexecute delay statements. When assessing the time complexity of delay-based algorithms, the question of whether delaysshould be counted arises. We consider both possibilities. Also of relevance is whether delay durations are upper-bounded.Again, we consider both possibilities. For each of these possibilities, we present an algorithm with either Θ(1) or Θ(log log N)time complexity. We also show that the Θ(log log N) algorithms that are given are asymptotically optimal by establishingmatching lower bounds. It follows from these results that the usage of delays can result in substantial improvements in RMRtime complexity, regardless of how one resolves the issues noted above. Work supported by NSF grants CCR 9972211, CCR 9988327, ITR 0082866, and CCR 0208289.