The Wrong Direction of Jensen’s Inequality Is Algorithmically Right

Author Or Zamir

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Author Details

Or Zamir
  • Princeton University, NJ, USA


The author would like to thank Avi Wigderson for pointing out important references.

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Or Zamir. The Wrong Direction of Jensen’s Inequality Is Algorithmically Right. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 107:1-107:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Let 𝒜 be an algorithm with expected running time e^X, conditioned on the value of some random variable X. We construct an algorithm A' with expected running time O (e^𝖤[X]), that fully executes 𝒜. In particular, an algorithm whose running time is a random variable T can be converted to one with expected running time O (e^𝖤[ln T]), which is never worse than O(𝖤[T]). No information about the distribution of X is required for the construction of 𝒜'.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Algorithm design techniques
  • Theory of computation → Computational complexity and cryptography
  • algorithms
  • complexity
  • Jensen’s inequality


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