On the space complexity of randomized synchronization
Journal of the ACM (JACM)
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Abstract. A snapshot scan algorithm takes an "instantaneous" picture of a region of shared memory that may he updated by concurrent processes. Many complex shared memory algorithms can be greatly simplified by structuring them around the snapshot scan abstraction. Unforinnately, the substantial decrease in conceptual complity is quite often counterbalanced by an increase in computational complexity. In this paper, we introduce the notion of a weak snapshot scan, a slightly weaker primitive that has a more efficient implementation. We propose the following methodology for using this abstraction: first, design and verify an algorithm using the more powerful snapshot scan, and second, replace the more powerful but less efficient snapshot with the weaker but more efficient snapshot, and show that the weaker abstraction nevertheless suffices to ensure the correctness of the enclosing algorithm. We give two examples of algorithms whose performance can be enhanced while retaining a simple modular structure: bounded concurrent timestamping, and bounded randomized consensus. The resulting timestamping protocol is the fastest known bounded concurrent timestamping protocol. The resulting randomized consensus protocol matches the computational complexity of the best known protocol that uses only bouned values.