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 $2^{o(m)}$.

翻译：NP-Hardness 3DM的标准证明提供了将3SAT减为3DM的4美元功率。在本说明中,我们提供了线性时间减值。在指数时间假设下,这种减值将运行时间下限从2美元(根据标准减值)减为2美元(根据标准减值)减为2美元(m)美元。