高围长MaxCut的显式向量算法
An explicit vector algorithm for high-girth MaxCut
摘要：
我们给出了MaxCut的一个近似算法，并保证了周长为$\geq 2k$的$d$ -正则图的平均边割分数。对于每一个$d \geq 3$和$k \geq 4$，我们的近似保证优于所有其他的经典和量子算法已知的作者。我们的算法构造了一个明确的向量解的标准半定松弛的MaxCut和超平面舍入。它可以被看作是一个简化的以前最好的已知的技术，它近似高斯波过程的无限$d$ -正则树。
英文摘要：
We give an approximation algorithm for MaxCut and provide guarantees on the average fraction of edges cut on $d$-regular graphs of girth $\geq 2k$. For every $d \geq 3$ and $k \geq 4$, our approximation guarantees are better than those of all other classical and quantum algorithms known to the authors. Our algorithm constructs an explicit vector solution to the standard semidefinite relaxation of MaxCut and applies hyperplane rounding. It may be viewed as a simplification of the previously best known technique, which approximates Gaussian wave processes on the infinite $d$-regular tree.
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