4 vs 7稀疏无向未加权直径在时间n4/3是SETH-hard

ACM Transactions on Algorithms (TALG) Pub Date : 2021-01-07 DOI:10.1145/3494540

Édouard Bonnet

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引用次数: 8

摘要

我们证明，假设强指数时间假设，对于每一个ε > 0，在7/4 - ε范围内近似n顶点m边图上的无向未加权直径需要m4/3 - 0(1)时间，即使当m = Õ(n)。这是第一个有条件地排除无向直径的近线性时间5/3近似的结果。

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4 vs 7 Sparse Undirected Unweighted Diameter Is SETH-hard at Time n4/3

We show, assuming the Strong Exponential Time Hypothesis, that for every ε > 0, approximating undirected unweighted Diameter on n-vertex m-edge graphs within ratio 7/4 - ε requires m4/3 - o(1) time, even when m = Õ(n). This is the first result that conditionally rules out a near-linear time 5/3-approximation for undirected Diameter.

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ACM Transactions on Algorithms (TALG)

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