Inapproximability of Diameter in Super-Linear Time: Beyond the 5/3 Ratio

Author Édouard Bonnet

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Édouard Bonnet
  • Univ. Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP UMR5668, France

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Édouard Bonnet. Inapproximability of Diameter in Super-Linear Time: Beyond the 5/3 Ratio. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 17:1-17:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We show, assuming the Strong Exponential Time Hypothesis, that for every ε > 0, approximating directed Diameter on m-arc graphs within ratio 7/4 - ε requires m^{4/3 - o(1)} time. Our construction uses non-negative edge weights but even holds for sparse digraphs, i.e., for which the number of vertices n and the number of arcs m satisfy m = O˜(n). This is the first result that conditionally rules out a near-linear time 5/3-approximation for a variant of Diameter.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Diameter
  • inapproximability
  • SETH lower bounds
  • k-Orthogonal Vectors


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