Thomas H. Spencer
Abstract
Some parallel algorithms have the property that, as they are allowed to take more time, the total work that they do is reduced. This paper describes several algorithms with this property. These algorithms solve important problems on directed graphs, including breadth-first search, topological sort, strong connectivity, and and the single source shorest path problem. All of the algorithms run on the EREW PRAM model of parallel computer, except the algorithm for strong connectivity, which runs on the probabilistic EREW PRAM.
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Index Terms
- Time-work tradeoffs for parallel algorithms
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Reviews
Linda Pagli
Problems on graphs—such as the directed spanning tree, breadth-first search, topological sort, cycle detection for directed graphs, strongly connected components, and single-source shortest paths with nonnegative edge lengths—are classic examples of problems for which no time-efficient parallel algorithm exists, although their sequential solutions are linear or almost linear. In this paper, Spencer observes that, if we do not search for the time-optimal algorithm but allow slower algorithms, we can obtain a better processor-time product (work) for the parallel algorithm. This basic idea makes it possible to define algorithms that exhibit time-work tradeoffs, which means that the slower the algorithms are allowed to be, the less work they do. The proposed parallel solutions for the above problems apply for a number of processors that vary in a given range. All of the algorithms are developed in the EREW PRAM model except for the one computing strong connectivity, which runs on the probabilistic EREW PRAM. This paper is of mainly theoretical interest.
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