Controlling and Assessing Correlations of Cost Matrices in Heterogeneous Scheduling

Abstract

Abstract. This paper considers the problem of allocating independent tasks to unrelated machines such as to minimize the maximum completion time. Testing heuristics for this problem requires the generation of cost matrices that specify the execution time of each task on each machine. Numerous studies showed that the task and machine heterogeneities belong to the properties impacting heuristics performance the most. This study focuses on orthogonal properties, the average correlations between each pair of rows and each pair of columns, which is a proximity measure with uniform instances 1 . Cost matrices generated with a novel generation method show the effect of these correlations on the performance of several heuristics from the literature. In particular, EFT performance depends on whether the tasks are more correlated than the machines and HLPT performs the best when both correlations are close to one.

Controlling the correlation of cost matrices to assess scheduling algorithm performance on heterogeneous platforms

“…The proofs of the analysis of the range‐based and CVB methods (Propositions to ) are in the companion research report …”

“…Correlation properties ( ρ task and ρ mach ) of cost matrices used in the literature (adapted from Canon et al). The correlations for the SPEC benchmarks belong to an area that is not well covered…”

“…A subset of the heuristics from Canon and Philippe was used with instances generated using the correlation noise‐based and combination‐based methods. The 3 selected heuristics, which are detailed in Canon et al,, Appendix E are based on distinct principles to emphasize how the correlation properties may have different effects on the performance.…”

“…*The related code, data, and analysis are available in Canon et al 17 Most of these results are also available in the companion research report 18 and in a conference paper. 1 † Ratio of the standard deviation to the mean.…”

“…A preliminary version of this work appeared in Euro‐Par 2016 . The current article extends it with more detailed proofs in the analysis of existing generation methods, a new generation method, and additional experiments and analysis of the behavior of scheduling heuristics.…”