Abstract
An Asynchronous PRAM allows processors to run at different and unpredictable speeds. Thus a fundamental problem in designing asynchronous PRAM algorithms is constructing a synchronization primitive which determines that a set of tasks has been completed. The Certified Write All Problem (CWA) is: given an array A[1..n] and a flag f which are both initialized to zero, set all elements of A to one, and then set f to one. A solution to the Certified Write All problem can be used as a synchronization primitive in a wide variety of settings. This paper investigates the complexity of CWA algorithms by presenting several new algorithms and lower bound proofs.
We present a new randomized CWA algorithm which uses expected O(n) work using up to n/log n processors. We show that this algorithm is optimal in both work and processor utilization by proving an Ω(n + p log n) lower bound on the expected work done by a p processor randomized CWA algorithm. Our CWA algorithm uses concurrent reads and concurrent writes. We show that this is necessary by proving that no concurrent read exclusive write (CREW) asynchronous PRAM can solve the CWA problem. However, for a fail-stop PRAM, where processors operate synchronously until they fail, we present a randomized CREW CWA algorithm. This algorithm also uses O(n) expected work using up to n/log n CREW fail-stop processors.
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© 1992 Springer-Verlag Berlin Heidelberg
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Martel, C., Subramonian, R. (1992). On the complexity of Certified Write All Algorithms. In: Shyamasundar, R. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1992. Lecture Notes in Computer Science, vol 652. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56287-7_119
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DOI: https://doi.org/10.1007/3-540-56287-7_119
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