Abstract

The problem of performing t tasks on n asynchronous or undependable processors is a basic problem in parallel and distributed computing. We consider an abstraction of this problem called the WriteAl l problem---using n processors write 1's into all locations of an array of size t. The most e#cient known deterministic asynchronous algorithms for this problem are due to Anderson and Woll. The first class of algorithms has work complexity of O(t ), for n t and any #>0, and they are the best known for the full range of processors (n = t). To schedule the work of the processors, the algorithms use lists of q permutations on [q](q n) that have certain combinatorial properties. Instantiating such an algorithm for a specific # either requires substantial pre-processing (exponential in 1/# )to find the requisite permutations, or imposes a prohibitive constant (exponential in 1/# ) hidden by the asymptotic analysis. The second class deals with the specific case of t = n 2, and these algorithms have work complexity of O(t log t). They also use lists of permutations with the same combinatorial properties. However instantiating these algorithms requires exponential in n preprocessing to find the permutations. To alleviate this costly instantiation Kanellakis and Shvartsman proposed a simple way of computing the permutations. They conjectured that their construction has the desired properties but they provided no analysis. In this paper

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