We consider the problem of approximating the arboricity of a graph $G= (V,E)$, which we denote by $\mathsf{arb}(G)$, in sublinear time, where the arboricity of a graph is the minimal number of forests required to cover its edges. An algorithm for this problem may perform degree and neighbor queries, and is allowed a small error probability. We design an algorithm that outputs an estimate $\hat{\alpha}$, such that with probability $1-1/\textrm{poly}(n)$, $\mathsf{arb}(G)/c\log^2 n \leq \hat{\alpha} \leq \mathsf{arb}(G)$, where $n=|V|$ and $c$ is a constant. The expected query complexity and running time of the algorithm are $O(n/\mathsf{arb}(G))\cdot \textrm{poly}(\log n)$, and this upper bound also holds with high probability. %($\widetilde{O}(\cdot)$ is used to suppress $\textrm{poly}(\log n)$ dependencies). This bound is optimal for such an approximation up to a $\textrm{poly}(\log n)$ factor.

翻译：我们考虑接近一个图形$G = (V,E) 的偏差率问题, 我们用美元表示, 在亚线性时间里, 图表的偏差值是覆盖其边缘所需的森林最小数量。 这个问题的算法可以执行程度和邻接查询, 并允许一个小错误概率。 我们设计一种算法, 计算出一个$( $) 的计算结果, 概率为 1-1/\ textrr{poly} (n) 美元, 概率为$\ mathsf{arb} (G) / c\log_ 2 n\leq\ hat\ hallpha}\\\ leq\ maths f{arb} (G) 最小值, 美元和 美元是恒定值的。 预期查询复杂度和运行时间是 $(n/ mostf{ar} (G)\ textr\ text$( ) $( 美元)\ colum\ detray a.