The approximation ratio of the longest processing time (LPT) scheduling algorithm has been investigated in various studies. While the tight approximation ratio is known for the cases when all processors are identical, the ratio is unknown when the processors have different speeds. In this study, we provide a tight approximation ratio for three, four, and five processors. We show that the ratios for these cases are no larger than the lower bound provided by Gonzalez et al. (1977) [14]. The ratios are approximately 1.38, 1.43, and 1.46 for three, four, and five processors, respectively.

中文翻译：

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少量不同处理器上LPT调度的最坏情况分析

最长处理时间（LPT）调度算法的近似率已在各种研究中进行了研究。虽然在所有处理器相同的情况下紧密逼近比率是已知的，但当处理器具有不同速度时该比率是未知的。在本研究中，我们为三个、四个和五个处理器提供了严格的近似比。我们表明这些情况的比率不大于 Gonzalez 等人提供的下限。（1977）[14]。对于三个、四个和五个处理器，该比率分别约为 1.38、1.43 和 1.46。