Hundreds of impossibility results for distributed computing
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Writing-all deterministically and optimally using a non-trivial number of asynchronous processors
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Writing-all deterministically and optimally using a nontrivial number of asynchronous processors
ACM Transactions on Algorithms (TALG)
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Traditional theoretical shared memory parallel models have been based on a number of assumptions which simultaneously simplify solutions to problems and distance the models from actual parallel machines. One such assumption is that processors work together in a synchronous fashion. Recent work has focused on finding a model that captures the essence of computation by processors communicating asynchronously through shared memory. In this paper, a general framework and set of criteria used to analyze these models, including the complexity analysis of several fundamental algorithmic paradigms, are considered. A general asynchronous model is introduced and how it satisfies these criteria is demonstrated. In this model, $O(\log p)$ algorithms are demonstrated for solving $p$-input versions of the problems of AND, OR, parity, maximum, minimum, and list ranking. To handle list ranking, a technique of analyzing algorithms is developed in which the set of tasks that are to be executed depends on the processor schedules.