Controlling memory access concurrency in efficient fault-tolerant parallel algorithms

The crcw pram with dynamic fail-stop errors is a faultprone multiprocessor model for which it is possible to control memory access redundancy while guaranteeing the reliability of efficient algorithms. Concurrent common reads and writes are necessary to handle dynamic faults and in this paper we show how to significantly decrease this concurrency and how to bound it in terms of the number of processor faults. We describe a low concurrency, efficient, and fault-tolerant algorithm for the Write- All primitive: “using ≤ N processors, write 1’s into N locations”. This primitive serves as the basis for efficient faulttolerant simulations of algorithms written for fault-free prams on faultprone prams. For any dynamic failure pattern F, our algorithm has total write concurrency ≤ |F| and total read concurrency ≤7 |F| log N, where |F| is the number of processor faults (e.g. no concurrency in a run without failures). Previous algorithms used Ω (N log N) concurrency even in the absence of faults. We also present an optimal fault-tolerant erew pram algorithm for Write-All when all processor faults are initial.