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arXiv · 0904.4512

Bounds on series-parallel slowdown

András Z. Salamon·Vashti Galpin
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Abstract

We use activity networks (task graphs) to model parallel programs and consider series-parallel extensions of these networks. Our motivation is two-fold: the benefits of series-parallel activity networks and the modelling of programming constructs, such as those imposed by current parallel computing environments. Series-parallelisation adds precedence constraints to an activity network, usually increasing its makespan (execution time). The slowdown ratio describes how additional constraints affect the makespan. We disprove an existing conjecture positing a bound of two on the slowdown when workload is not considered. Where workload is known, we conjecture that 4/3 slowdown is always achievable, and prove our conjecture for small networks using max-plus algebra. We analyse a polynomial-time algorithm showing that achieving 4/3 slowdown is in exp-APX. Finally, we discuss the implications of our results.

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András Z. Salamon, Vashti Galpin. 2009-04-29. Bounds on series-parallel slowdown. https://arxiv.org/abs/0904.4512

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