An efficient Write-All algorithm for fail-stop PRAM without initialized memory

Abstract

The problem of Write-All—using P processors to write 1's into all locations of an array of size N, where P ⩽ N—has been used as the basic building block for constructing efficient and fault-tolerant parallel algorithms. All previous Write-All solutions use Ω( P) auxiliary shared memory and assume that this memory is cleared or initialized to some known value. When Write-All building blocks are used in polylogarithmic parallel time algorithms, auxiliary memory initialization cannot be amortized over the computation. Thus, assuming clear memory is a very strong precondition, and for Write-All itself raises a legitimate “chicken-or-egg” objection. Using a determistic bootstraping and balancing argument, we show how to Write-All when auxiliary memory is contaminated with arbitrary values. For any dynamic pattern of fail-stop, no-restart errors on a CRCW PRAM with at least one surviving processor, our new algorithm writes all 1's using O( N + Plog 3N (loglog N) 2 ) work, without any initialization assumption. This technique can be combined with any Write-All algorithm to yield efficient simulations of any PRAM and even optimal simulations given processor slack. It can also be used with restartable fail-stop processor simulations.