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• W3208586193 abstract "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 $1-1/textrm{poly}(n)$, $mathsf{arb}(G)/clog^2 n leq hat{alpha} leq mathsf{arb}(G)$, 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." @default.
• W3208586193 created "2021-11-08" @default.
• W3208586193 creator A5053488431 @default.
• W3208586193 creator A5063746987 @default.
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• W3208586193 date "2021-10-28" @default.
• W3208586193 modified "2023-09-27" @default.
• W3208586193 title "Approximating the Arboricity in Sublinear Time." @default.
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• W3208586193 hasPublicationYear "2021" @default.
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