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

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 نشر من قبل \\'Edouard Bonnet
 تاريخ النشر 2021
  مجال البحث الهندسة المعلوماتية
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 تأليف Edouard Bonnet




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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 $m^{4/3 - o(1)}$ time. This is the first result that conditionally rules out a near-linear time $5/3$-approximation for undirected Diameter.



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