Correlation-Aware Heuristics for Evaluating the Distribution of the Longest Path Length of a DAG with Random Weights
Résumé
Coping with uncertainties when scheduling task graphs on parallel machines requires to perform non-trivial evaluations. When considering that each computation and communication duration is a random variable, evaluating the distribution of the critical path length of such graphs involves computing maximums and sums of possibly de- pendent random variables. The discrete version of this evaluation problem is known to be #P- hard. Here, we propose two heuristics, CorLCA and Cordyn, to compute such lengths. They ap- proximate the input random variables and the intermediate ones as normal random variables, and they precisely take into account correlations with two distinct mechanisms: through lowest common ancestor queries for CorLCA and with a dynamic programming approach for Cordyn. Moreover, we empirically compare some classical methods from the literature and confront them to our solutions. Simulations on a large set of cases indicate that CorLCA and Cordyn consti- tute each a new relevant trade-off in terms of rapidity and precision.
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