Abstract
We evaluate the average-case performance of three approximation algorithms for online non-clairvoyant scheduling of parallel tasks with precedence constraints. We show that for a class of wide task graphs, when task sizes are uniformly distributed in the range [1₀C], the online non-clairvoyant scheduling algorithm LL-SIMPLE has an asymptotic average-case performance bound of M/(M-(3-(1 + 1/C)C+1)C-1), where M is the number of processors. For uniform probability distributions of task sizes, we present numerical and simulation data to demonstrate the accuracy of our general asymptotic average-case performance bound. We also report extensive experimental results on the average-case performance of online non-clairvoyant scheduling algorithms LL-GREEDY and LS. Algorithm LL-GREEDY has better performance than LL-SIMPLE using an improved algorithm to schedule independent tasks in the same level. Algorithm LS produces even better schedules due to a break of boundaries among levels.
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