In high performance computing, scheduling of tasks and allocation to machines is very critical especially when we are dealing with heterogeneous execution costs. Simulations can be performed with a large variety of environments and application models. However, this technique is sensitive to bias when it relies on random instances with an uncontrolled distribution. We use methods from the literature to provide formal guarantee on the distribution of the instance. In particular, it is desirable to ensure a uniform distribution among the instances with a given task and machine heterogeneity. In this article, we propose a method that generates instances (cost matrices) with a known distribution where tasks are scheduled on machines with heterogeneous execution costs.
How to generate instances with relevant properties and without bias remains an open problem of critical importance for a fair comparison of heuristics. In the context of scheduling with precedence constraints, the instance consists of a task graph that determines a partial order on task executions. To avoid selecting instances among a set populated mainly with trivial ones, we rely on properties that quantify the characteristics specific to difficult instances. Among numerous identified such properties, the mass measures how much a task graph can be decomposed into smaller ones. This property, together with an in-depth analysis of existing random task graph generation methods, establishes the sub-exponential generic time complexity of the studied problem. Empirical observations on the impact of existing generation methods on scheduling heuristics concludes our study.
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