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arXiv · 2101.02312

4 vs 7 sparse undirected unweighted Diameter is SETH-hard at time $n^{4/3}$

Édouard Bonnet
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Abstract

We show, assuming the Strong Exponential Time Hypothesis, that for every $\varepsilon > 0$, approximating undirected unweighted Diameter on $n$-vertex $n^{1+o(1)}$-edge graphs within ratio $7/4 - \varepsilon$ requires $n^{4/3 - o(1)}$ time. This is the first result that conditionally rules out a near-linear time $5/3$-approximation for undirected Diameter.

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Édouard Bonnet. 2021-01-07. 4 vs 7 sparse undirected unweighted Diameter is SETH-hard at time $n^{4/3}$. https://arxiv.org/abs/2101.02312

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