On the complexity of certified write all algorithms

Abstract

An Asynchronous PRAM allows processors to run at different and unpredictable spccds. Thus a fundamental problem in designing asynchronous PRAM algorithms is constructing a synchronization primitive which determines that a set of tasks has been complctcd. The Certified Write All Problem (CWA) is: given an array A[1..n] and a flag f which arc both initialized to zero, set all clemcnts 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 Mgorithms and lower bound proofs. We present a new randomized CWA algorithm which uses expected O(n) work ushlg 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 concurrcnt reads and concurrent writes. We show that this is necessary by proving that no concurrent read exclusive write (CREW) asynchronous PItAM can solvc the CWA problem. However, for a fail-stop PRAM, where processors opcrate 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 CREVr fail-stop processors.