Timing-Based Mutual Exclusion with Local Spinning
We consider the time complexity of shared-memory mutual exclusion algorithms based on reads, writes, and comparison primitives under the remote-memory-reference (RMR) time measure. For asynchronous systems, a lower bound of Ω(log N/log log N) RMRs per critical-section entry has been established in previous work, where N is the number of processes. In this paper, we show that lower RMR time complexity is attainable in semi-synchronous systems in which processes may execute delay statements. When assessing the time complexity of delay-based algorithms, the question of whether delays should be counted arises. We consider both possibilities. Also of relevance is whether delay durations are upper-bounded. (They are lower-bounded by definition.) 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. For the cases in which a Ω(log log N) algorithm is given, we establish matching Ω(log log N) lower bounds.
KeywordsTime Complexity Visible Process Critical Event Critical Section Mutual Exclusion
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