One of the first attempts at the automation of test case reduction was the minimizing delta debugging algorithm, widely known as ddmin. Despite its age, it is still an unavoidable cornerstone of this field of research. One criticism against ddmin is that it can take too long to reach the granularity where it can perform actual reduction. Therefore, in this paper, ddmin is generalized with respect to the granularity by introducing a new split factor parameter, leading to the formalization of a parametric algorithm variant. The complexity analysis of this parametric variant reveals that the theoretical worst and best-case behavior of ddmin can be improved. Moreover, the results of experiments with the generalized algorithm show that the reduction can be sped up significantly by choosing the right split factor: up to 84% of the test steps can be eliminated in practice.
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