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

Édouard Bonnet (1, 2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 ENS de Lyon - École normale supérieure de Lyon

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 m^4/3−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.

Mots clés: Diameter; inapproximability; SETH lower bounds; k-Orthogonal Vectors

Domaines: Informatique [cs]

Édouard Bonnet. 4 vs 7 sparse undirected unweighted Diameter is SETH-hard at time n^4/3. ICALP 2021, Jul 2021, Glasgow, United Kingdom. ⟨10.4230/LIPIcs.ICALP.2021.24⟩. ⟨hal-03430322⟩