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

Abstract

We show, assuming the Strong Exponential Time Hypothesis, that for every $\epsilon >0$, approximating undirected unweighted Diameter on $n$-vertex $n^{1+o(1)}$-edge graphs within ratio $7/4-\epsilon$ 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.

arXiv comment15 pages, 3 figures