The standard proof of NP-Hardness of 3DM provides a power-$4$ reduction of 3SAT to 3DM. In this note, we provide a linear-time reduction. Under the exponential time hypothesis, this reduction improves the runtime lower bound from $2^{o(\sqrt[4]{m})}$ (under the standard reduction) to $2^{o(m)}$.

中文翻译：

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三维匹配是NP-Hard

3DM 的 NP 硬度的标准证明提供了从 3SAT 到 3DM 的功率降低 4 美元。在本说明中，我们提供了线性时间减少。在指数时间假设下，这种减少将运行时下限从 $2^{o(\sqrt[4]{m})}$（在标准减少下）提高到 $2^{o(m)}$。